One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.

A complete recursive description of noetherian linear _KL_-algebras is given. _L_-algebras form a quantum structure that occurs in algebraic logic, combinatorial group theory, measure theory, geometry, and in connection with solutions to the Yang-Baxter equation. It is proved that the self-similar closure of a noetherian linear _KL_-algebra is determined by its partially ordered set of primes, and that its elements admit a unique factorization by a decreasing sequence of prime elements.

Priming of lineage‐specific genes in pluripotent embryonic stem cells facilitates rapid and coordinated activation of transcriptional programmes during differentiation. There is growing evidence that pluripotency factors play key roles in priming tissue‐specific genes and in the earliest stages of lineage commitment. As differentiation progresses, pluripotency factors are replaced at some primed genes by related lineage‐specific factors that bind to the same sequences and maintain epigenetic priming until the gene is activated. Polycomb and trithorax group proteins bind many genes in pluripotent (...) cells generating bivalent domains that contain both active and repressive histone modifications. The properties of polycomb proteins suggest that they act as gatekeepers, helping to maintain silencing in pluripotent stem cells while establishing a chromatin environment that is permissive for priming by sequence‐specific factors. The overall effect of factor‐mediated priming is to initiate the input of information required for cell differentiation before the first lineage choices have been made. (shrink)

The COVID-19 pandemic has negatively impacted the psychosocial functioning of children and families. It is important to consider adversity in relation to processes of positive adaptation. To date, there are no empirically validated multi-item scales measuring COVID-related positive adaptation within families. The aim of the current study was to develop and validate a new measure: the Family Positive Adaptation during COVID-19 Scale. The sample included 372 female and 158 male caregivers of children ages 5–18 years old from the United Kingdom, (...) the United States, Canada, and Australia, who completed measures in May 2020. Participants responded to a 14-item survey indexing a range of perceived coping and adaptation behaviors at the beginning of the pandemic. An exploratory factor analysis yielded an optimal one-factor solution comprised of seven items related to family cohesion, flexibility, routines, and meaning-making. Multigroup confirmatory factor analysis demonstrated measurement invariance across female and male caregivers, demonstrating that the factor structure, loadings, and thresholds did not vary by caregiver sex. There was evidence for concurrent validity with significant bivariate correlations between the Family PACS scores and measures of caregiver positive coping, parenting practices, couple satisfaction, and family functioning, but not negatively-valenced constructs. Findings inform our conceptualization of how families have adapted to adverse pandemic-related conditions. Further, we provide preliminary support for the Family PACS as a practical tool for evaluating positive family adaptation during this global crisis, with implications for future widespread crises. (shrink)

We show that $\mathrm{IE}_1$ proves that every element greater than 1 has a unique factorization into prime powers, although we have no way of recovering the exponents from the prime powers which appear. The situation is radically different in Bezout models of open induction. To facilitate the construction of counterexamples, we describe a method of changing irreducibles into powers of irreducibles, and we define the notion of a frugal homomorphism into $\hat\mathbb{Z} = \Pi_p\mathbb{Z}_p$, the product of the $p$-adic (...) integers for each prime $p$. (shrink)

Clark reports on a variationist analysis of intervocalic word‐medial /t/ from recorded spontaneous speech monologues. The results provide evidence that tokens are more likely to be realized as voiced if the preceding token was voiced, an effect which is weaker with increased temporal distance between the prime and target.

We show that IE1 proves that every element greater than 1 has a unique factorization into prime powers, although we have no way of recovering the exponents from the prime powers which appear. The situation is radically different in Bézout models of open induction. To facilitate the construction of counterexamples, we describe a method of changing irreducibles into powers of irreducibles, and we define the notion of a frugal homomorphism into Ẑ = ΠpZp, the product of the p-adic (...) integers for each prime p. (shrink)

In many simple integral domains, such as Z or Z[i], there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact that such a naive approach does not immediately translate to integral domains like Z[x] or the ring of integers in an algebraic number field, there still exist computational procedures that work to determine the prime elements in these cases. In contrast, we (...) will show how to computably extend Z in such a way that we can control the ordinary integer primes in any Π20 way, all while maintaining unique factorization. As a corollary, we establish the existence of a computable unique factorization domain such that the set of primes is Π20-complete in every computable presentation. (shrink)

It is often assumed that believing that p for a normative reason consists in nothing more than (i) believing that p for a reason and (ii) that reason’s corresponding to a normative reason to believe that p, where (i) and (ii) are independent factors. This is the Composite View. In this paper, we argue against the Composite View on extensional and theoretical grounds. We advocate an alternative that we call the Prime View. On this view, believing for a normative (...) reason is a distinctive achievement that isn’t exhausted by the mere conjunction of (i) and (ii). Its being an achievement entails that (i) and (ii) are not independent when one believes for a normative reason: minimally, (i) must hold because (ii) holds. Apart from its intrinsic interest, our discussion has important upshots for central issues in epistemology, including the analysis of doxastic justification, the epistemology of perception, and the place of competence in epistemology. (shrink)

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...) program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect. (shrink)

By hypothesis, awareness is involved in the modulation of feedback from semantics to the lexical level in the visual word recognition system. When subjects are aware of the fact that there are many related prime–target pairs in a semantic priming experiment, this knowledge is used to configure the system to feed activation back from semantics to the lexical level so as to facilitate processing. When subjects are unaware of this fact, the default set is maintained in which activation is (...) not fed back from semantics to the lexical level so as to conserve limited resources. Qualitative differences in the pattern of data from two lexical decision experiments that employ masked priming are consistent with this hypothesis. Semantic context and stimulus quality interact when the prime is processed with awareness whereas these same two factors produce additive effects on RT when the prime is unlikely to have been processed with awareness. These experiments thus illustrate one way in which awareness affects the dynamics of visual word recognition. (shrink)

Using self-report as a measure of conscious experience has been a point of contention in mind wandering research. Whereas prior work has focused on the introspective component of self-report validity, the current research introduces an honesty prime task to the current paradigm in order to assess the role of goal states and social factors on self-report accuracy. Findings provide evidence for an inflated report of mind wandering frequency arising from demand characteristics, intensified by the divergent properties of the subjective (...) and behavioural measures and the general deficit in meta-awareness of off task episodes. (shrink)

The present study examines the effect of priming on business ethical decision making. Priming is based on the idea that our perceptions, actions, and emotions are distorted by unconscious cues from our environment. Subjects were primed for either “politeness” or “rudeness” using a sentence completion task. Following the priming, the subjects were asked to react to a series of ethical scenarios. The results showed that subjects primed for “rudeness” perceived the scenarios as less unethical than subjects primed for “politeness”. Similar (...) results were observed in both the American and the Dominican samples. The results indicate that business ethical decision making is influenced by environmental factors we are unaware off. (shrink)

Objectives: Treatment decisions in ethically complex situations are known to depend on a physician's personal characteristics and medical experience. We sought to study variability in decisions to withdraw or withhold specific life-supporting treatments in terminal care and to evaluate the association between decisions and such background factors.Design: Readiness to withdraw or withhold treatment options was studied using a terminal cancer patient scenario with alternatives. Physicians were asked about their attitudes, life values, experience, and training; sociodemographic data were also collected.Setting: Finnish (...) physicians, postal survey.Survey sample: Five hundred general practitioners, 300 surgeons, 300 internists, and 82 oncologists.Results: Treatments most often forgone were blood transfusion and thrombosis prophylaxis . Least willingly abandoned were intravenous hydration and supplementary oxygen . Female doctors were less likely to discontinue thrombosis prophylaxis and supplementary oxygen , but more readily x ray and laboratory examinations. Young doctors were more likely to continue antibiotics , thrombosis prophylaxis , supplementary oxygen and laboratory tests . Oncologists comprised the specialty most ready to forgo all studied treatments except antibiotics and blood transfusion. The family's wishes significantly increased treatment activity. Young and female practitioners and oncologists were most influenced by family appeal. Advance directives made decisions significantly more reserved and uniform. Different factors in the physician's background were found to predict decisions to withdraw antibiotics or IV hydration.Conclusion: The considerable variation observed in doctors' decisions to forgo specific life-sustaining treatments was seen to depend on their personal background factors. Experience, supervision, and postgraduate education seemed to be associated with more reserved treatment decisions. To increase the objectivity of end of life decisions, training, and research are of prime significance in this ethically complex area of medicine. (shrink)

Natural language involves both speaking and listening. Recent models claim that production and comprehension share aspects of processing and are linked within individuals (Dell & Chang, 2014; MacDonald, 2013; Pickering & Garrod, 2004; 2013a). Evidence for this claim has come from studies of cross-modality structural priming, mainly examining processing in the direction of comprehension to production. The current study replicated these comprehension to production findings and developed a novel cross-modal structural priming paradigm from production to comprehension using a temporally-sensitive online (...) measure of comprehension, Event-Related Potentials. For Comprehension-to-Production priming, participants first listened to active or passive sentences and then described target pictures using either structure. In Production-to-Comprehension priming, participants first described a picture using either structure and then listened to target passive sentences while EEG was recorded. Comprehension-to-Production priming showed the expected passive sentence priming for syntactic choice, but not response time or average syllable duration. In Production-to-Comprehension priming, primed, versus unprimed, passive sentences elicited a reduced N400. These effects support the notion that production and comprehension share aspects of processing and are linked within the individual. Moreover, this paradigm can be used for the exploration priming at different linguistic levels as well as the influence of extra-linguistic factors on natural language use. (shrink)

Although structural priming has been considered to be an independent cognitive process, recent evidence suggests that structural priming is modulated by sociocognitive factors such as social perception; speakers are more likely to mimic the sentence structure of a socially desirable interlocutor than the structure of a less desirable interlocutor. This study aims to further address the role of sociocognitive factors in language use by investigating how individual differences in social perception and tendency to align with others modulate same-verb structural priming. (...) In particular, we investigate how likely students are to repeat a sentence structure of a teacher depending on their perception of the teacher and their social monitoring tendency. Our results demonstrate that students’ tendency to imitate a sentence structure of the teacher is positively influenced by their perception of the teacher but negatively by social monitoring. We suggest that the effects may be accounted for in terms of their influence on attention and memory encoding. (shrink)

Translation equivalents for cognates in different script systems share the same meaning and phonological similarity but are different orthographically. Event-related potentials were recorded during the visual recognition of cross-script cognates and non-cognates together with concreteness factors while Chinese learners of English performed a lexical decision task with the masked translation priming paradigm in Experiment 1 and Experiment 2. N400 effect was found to be closely related to priming effects of cross-script cognate status and concreteness in Experiment 1; and in Experiment (...) 2, N150 and N400 effects were related to priming effects of cross-script cognate status and concreteness, and greater priming effects of cross-script cognate status in cognates than in non-cognates for abstract words were found in the time window of 100–200 ms. Meanwhile, the asymmetry of translation directions was observed in smaller priming effects in forward translation than in backward translation in the time window of 100–200 ms for abstract cognates, and in larger priming effects in forward translation than in backward translation in the time window of 350–550 ms for each type of words. We discussed the roles of phonological activation and concreteness effects in view of the function of N150 and N400 components as well as the relevant models, mainly the Distributed Feature Model and Bilingual Interactive Activation model. (shrink)

Part of speech feature is the representation between syntactic morphology and semantic category. Priming effect experiment can test the correlation between the parts of speech feature and the lexical processing process. This article puts forward part of speech representation paradigmatic and syntagmatic effect hypotheses. The experiments applied the design pattern of 3 ∗ 2 ∗ 3. Subjects are requested to make options of the part of speech of the target words. This study shows that when Chinese English learners extract an (...) individual word, their choices are still influenced by part of speech factor without the restrictions of constructive syntagmatic semantic conditions. Both the syntagmatic and paradigmatic effects are verified. Part of speech priming effect intensity is influenced by the English acquisition levels of the subjects. (shrink)

Using the Stroop paradigm, we have previously shown that a specific suggestion can remove or reduce involuntary conflict and alter information processing in highly suggestible individuals . In the present study, we carefully matched less suggestible individuals to HSIs on a number of factors. We hypothesized that suggestion would influence HSIs more than LSIs and reduce the Stroop effect in the former group. As well, we conducted secondary post hoc analyses to examine negative priming – the apparent disruption of the (...) response to a previously-ignored item. Our present findings indicate that suggestion reduces Stroop effects in HSIs. Secondary analyses show that LSIs had an NP effect at baseline and that suggestion influenced the NP condition. Thus, at least in this experimental context, suggestion seems to dampen a deeply-engrained and largely automatic process – reading – by wielding a larger influence on HSIs relative to comparable LSIs. (shrink)

Accurately predicting other people's actions may involve two processes: internal real-time simulation (dynamic updating) and matching recently perceived action images (static matching). Using a priming of body parts, this study aimed to differentiate the two processes. Specifically, participants played a motion-controlled video game with either their arms or legs. They then observed arm movements of a point-light actor, which were briefly occluded from view, followed by a static test pose. Participants judged whether this test pose depicted a coherent continuation of (...) the previously seen action (i.e., “action prediction task”). Evidence of dynamic updating was obtained after compatible effector priming (i.e., arms), whereas incompatible effector priming (i.e., legs) indicated static matching. Together, the results support action prediction as engaging two distinct processes, dynamic simulation and static matching, and indicate that their relative contributions depend on contextual factors like compatibility of body parts involved in performed and observed action. (shrink)

Syntactic satiation is the phenomenon where some sentences that initially seem ungrammatical appear more acceptable after repeated exposures (Snyder 2000). We investigated satiation by manipulating two factors known to affect syntactic priming, a phenomenon where recent exposure to a grammatical structure facilitates subsequent processing of that structure (Bock 1986). Specifically, we manipulated (i) Proximity of exposure (number of sentences between primes and targets) and (ii) Lexical repetition (type of phrase repeated across primes and targets). Experiment 1 investigated whether acceptability ratings (...) of Complex-NP Constraint (CNPC) and Subject islands improve as consequence of these variables. If so, priming and satiation may be linked. When primes were separated from targets by one sentence, CNPC islands’ acceptability was improved by a preceding island of the same type, but Subject islands’ acceptability was not. When prime-target pairs were separated by five sentences, we found no improvement for either island type. Experiment 2 asked whether improvements in Experiment 1 reflected online processing or offline end-of-sentence effects. We used a self-paced reading paradigm to diagnose online structure-building and processing facilitation (Ivanova 2012) during processing. We found priming for Subject islands when primes and targets were close together, but not when they were further apart. No effects were detected when CNPC islands were close together, but there was a localized effect when sentences were further apart. The disjunction between Experiments 1 and 2 suggests repetition of the structure in Subject islands facilitated online processing but did not ‘spill over’ to acceptability ratings. Meanwhile, results for CNPC islands suggest that acceptability rating improvements in Experiment 1 may be driven by factors distinct from online processing facilitation. Together, our experiments show that satiation may not be a one-size-fit-all phenomenon but, instead, appears to manifest itself differently for different types of structures. Priming is possible and may be linked to satiation in some purportedly “unbuildable” structures (e.g. Subject islands), but not for all types (e.g. CNPC islands). Despite this, it appears that while the types of mechanisms targeting different island types are distinct, they are nevertheless similarly sensitive to the proximity between individual exposures. (shrink)

In this study, we examined whether the lexical competition process embraced by most models of spoken word recognition is sensitive to talker-specific information. We used a lexical decision task and a long lag priming experiment in which primes and targets sharing all phonemes except the last one were presented in two separate blocks of stimuli. In Experiment 1, the competitor prime block was presented only once to listeners, and no modulation of the competitor priming effect as a function of (...) a talker change between the primes and targets was observed. However, attenuation in the competitor priming effect in the case of a talker change between the primes and targets was observed in Experiment 2 in which the competitor prime block was presented five times to listeners. We discuss our findings in reference to hybrid models of spoken word recognition in which repetition of words with the same talker could be a key factor in the formation and access to talker-dependent representations. (shrink)

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.

Negative compatibility effects in the masked-prime paradigm are usually obtained when primes are masked effectively. With ineffective masks—and primes above the perceptual threshold—positive compatibility effects occur. We investigated whether this pattern reflects a causal relationship between conscious awareness and low-level motor control, or whether it reflects the fact that both are affected in the same way by changes in physical stimulus attributes. In a 5-session perceptual learning task, participants learned to consciously identify masked primes. However, they showed unaltered NCEs (...) that were not different from those produced by participants in a control group without equivalent perceptual learning. A control experiment demonstrated that no NCEs occur when prime identification is made possible by ineffective masking. The results suggest that perceptual awareness and low-level motor control are affected by the same factors, but are fundamentally independent of each other. (shrink)

While it is known that reward induces attentional prioritization, it is not clear what effect reward-learning has when associated with stimuli that are not fully perceived. The masked priming paradigm has been extensively used to investigate the indirect impact of brief stimuli on response behavior. Interestingly, the effect of masked primes is observed even when participants choose their responses freely. While classical theories assume this process to be automatic, recent studies have provided evidence for attentional modulations of masked priming effects. (...) Most such studies have manipulated bottom-up or top-down modes of attentional selection, but the role of “newer” forms of attentional control such as reward-learning and selection history remains unclear. In two experiments, with number and arrow primes, we examined whether reward-mediated attentional selection modulates masked priming when responses are chosen freely. In both experiments, we observed that primes associated with high-reward lead to enhanced free-choice priming compared to primes associated with no-reward. The effect was seen on both proportion of choices and response times, and was more evident in the faster responses. In the slower responses, the effect was diminished. Our study adds to the growing literature showing the susceptibility of masked priming to factors related to attention and executive control. (shrink)

Although Sign Languages are gestural languages, the fact remains that some linguistic information can also be conveyed by spoken components as mouthing. Mouthing usually tend to reproduce the more relevant phonetic part of the equivalent spoken word matching with the manual sign. Therefore, one crucial issue in sign language is to understand whether mouthing is part of the signs themselves or not, and to which extent it contributes to the construction of signs meaning. Another question is to know whether mouthing (...) patterns constitute a phonological or a semantic cue in the lexical sign entry. This study aimed to investigate the role of mouthing on the processing of lexical signs in French Sign Language (LSF), according the type of bilingualism (intramodal vs. bimodal). For this purpose, a behavioral sign-picture lexical decision experiment was designed. Intramodal signers (native deaf adults) and Bimodal signers (fluent hearing adults) have to decide as fast as possible whether a picture matched with the sign seen just before. Five experimental conditions in which the pair sign-mouthing were congruent or incongruent were created. Our results showed a strong interference effect when the sign-mouthing matching was incongruent, reflected by higher error rates and lengthened reaction times compared with the congruent condition. This finding suggests that both groups of signers use the available lexical information contained in mouthing during accessing the sign meaning. In addition, deaf intramodal signers were strongly interfered than hearing bimodal signers. Taken together, our data indicate that mouthing is a determining factor in LSF lexical access, specifically in deaf signers. (shrink)

Generally, the testimony of intoxicated witnesses has been considered relatively unreliable, but recent research has nuanced the knowledge base regarding these vulnerable witnesses.PurposeTo demonstrate the application of recent research findings regarding intoxicated witnesses to the statements made by a key witness to the murder of Olof Palme, Sweden's prime minister, in 1986. An additional purpose was to illustrate the use of a nuanced calculation of blood alcohol concentration for researchers.MethodsThe Palme murder has been debated since the crime was committed (...) and no one has yet been sentenced. One of the witnesses was intoxicated and to estimate a range for his BAC at the time, a comprehensive BAC calculation was conducted in this study to illustrate important factors to consider in these types of cases.ResultsThrough the demonstration of the use of a nuanced BAC formula and by applying recent research results from studies on intoxicated witnesses, it was estimated that the possible BAC of the witness in the Palme-case at the time of the witnessed crime ranged between BAC = 0 to BAC = 0.13, depending on the type of alcoholic beverage consumed and whether the witness was a social or heavy drinker. This puts the witness either well within the span of maintained completeness as well as maintained accuracy rate, or slightly exceeding this span into the BAC-range of reduced completeness but maintained accuracy rate. He was questioned immediately, and thereafter repeatedly, and he reported similar information throughout the interviews, which is in line with previous results on information maintenance over repeated interviews among intoxicated witnesses.ConclusionThe current case example shows how recent research on intoxicated witnesses can be applied in praxis, illustrating important factors for legal practitioners to consider when interpreting information from intoxicated witnesses. It also provides legal practitioners and researchers with an example of a structured approach to more nuanced BAC-calculations. (shrink)

We examine the role of socio-demographic factors on consumers’ pro-environmental behavior (PEB)–a subset of ethical behavior and analyze its implications in an emerging market, with a sample study from India. Multivariate analysis of variance (MANOVA) was performed as research method. Results show that males display higher PEB than their female counterparts. Married consumers score more on PEB than single. Mid-age consumers (36–50) also score high on PEB than young and old-age consumers. Furthermore, highly educated consumers are more pro-environmentalist than graduates (...) and post-graduates. The novelty of this study is that centers on the use of demographic variables interactively in order to form microsegments. For instance, married men score more on PEB scale than unmarried men and women and prefer green channels even more (i.e., public transportation). On the contrary, unmarried women display no hesitation in paying more for energy-efficient goods compared to married men and unmarried men. Marketers may aim in setting such PEBs as the moral standards among consumers being an easily identifiable segment as their prime target. (shrink)

We challenge the arguments of Cohen Kadosh & Walsh (CK&W) on two grounds. First, interactions between number form (e.g., notation, format, modality) and an experimental factor do not show that the notations/formats/modalities are processed separately. Second, we discuss evidence that numbers are coded abstractly, also when not required by task demands and processed unintentionally, thus challenging the authors' dual-code account.

The sheer impact of the recent global financial turmoil and scandals (such as Enron and WorldCom) has demonstrated that unbridled commercial entrepreneurs who are allowed to pursue their short-term opportunities regardless of the consequences has led to a massive depreciation of the wealth of nations, social livelihood and environmental degradation. This article suggests that the time has come for entrepreneurs to adopt a more integrative view of business that blends economic, social and environmental values. Social entrepreneurs present such a proposition (...) through their deep commitment towards the social vision, appreciation of sustainable practices, innovativeness, ability to build social networks and also generate viable financial returns. It could be expected that social entrepreneurs often possess certain distinct personality characteristics which define their behaviours/actions. Personality traits are partly developed by innate nurturing, socialization and education. These tacit traits are also formed values/beliefs held and play an important role in driving social entrepreneurial decision making. Thus, personality traits may influence the intentions and the manner in which the individual acts. We hold that if social entrepreneurship is to be effective and impactful, business and management education can facilitate the development of these critical personality traits. Thus, this study primes at determining the personality traits that influence social entrepreneurs’ start-up intentions. It also reinforces the findings that personality traits do influence entrepreneurship in general. This study examines the influence of the Big Five personality traits on social entrepreneurship dimensions. The findings reveal that agreeableness positively influences all dimensions of social entrepreneurship, whereas openness exerts a positive influence on social vision, innovation and financial returns. Methodologically, this study develops valid and reliable scales for social entrepreneurship and verifies the adopted Big Five personality measure of Schmit et al. (Pers Psychol 53:153–193, 2000) using the five-point Likert scale. The implication of this study is that element of appreciation of social responsibility, sustainability and character development needs to be integrated within the business education curriculum to support social entrepreneurs in realizing genuine value and impact to the causes and communities they serve. Future business leaders also need to be equipped with entrepreneurship skills, while exuding independent and reflective thinking in the pursuit life-long learning. The originality of this study lies in its focus on personality traits on social rather than commercial entrepreneurship. It is hoped that the findings will trigger a paradigm shift towards greater social entrepreneurship through education by nurturing sustainable development values in future business graduates. (shrink)

This book is written for middle and high school students, for teachers and for those with a passion for math, containing 150+1 problems (which are followed by solutions) to make it more accessible to the reader. The last problem (150+1), a very interesting one, leaves some space for comments and generalizations. The book is a collaboration between a multi-awarded student at Romania’s National Mathematics Olympiad (Carina Maria Viespescu, student in year 10 at Liceul International of Informatics Bucuresti), a teacher from (...) Colegiul National “Fratii Buzesti” din Cravoia and prof. Dr. Emeritus Florentin Smarandache from the University of New Mexico. A couple of problems are proposed by colleagues, and their names indicated in footnotes. (shrink)

Is alternative mathematics possible? More specifically,is it possible to imagine that mathematics could havedeveloped in any other than the actual direction? Theanswer defended in this paper is yes, and the proofconsists of a direct demonstration. An alternativemathematics that uses vague concepts and predicatesis outlined, leading up to theorems such as ``Smallnumbers have few prime factors''.

For each $p \geq 2$ there exists a model ${\bf M}^{*}$ of $I\Delta_{0}(\alpha)$ which satisfies the Count( $p$ ) principle. Furthermore, if $p$ contains all prime factors of $q$ there exist $n,r \in {\bf M}^{*}$ and a bijective map $f \in {\rm dom}({\bf M}^{*})$ mapping $\{1,2,\ldots,n\}$ onto $\{1,2,\ldo ts,n+q^{r}\}$ . A corollary is a complete classification of the Count( $q$ ) versus Count( $p$ ) problem. Another corollary shows that the pigeon-hole principle for injective maps does not follow from (...) any of the Count( $q$ ) principles. This solves an open question [Ajtai 94]. (shrink)

It is commonly held that the natural numbers sequence 0, 1, 2,... possesses a unique structure. Yet by a well known model theoretic argument, there exist non-standard models of the formal theory which is generally taken to axiomatize all of our practices and intentions pertaining to use of the term “natural number.” Despite the structural similarity of this argument to the influential set theoretic indeterminacy argument based on the downward L ̈owenheim-Skolem theorem, most theorists agree that the number theoretic version (...) does not have skeptical consequences about the reference of “natural number” analogous to the ‘relativity’ Skolem claimed pertains to notions such as “uncountable” and “cardinal.” In this paper I argue that recent proposals by Shapiro, Lavine, McGee and Field which aim to distinguish the number and set theoretic indeterminacy arguments by locating extra-mathematical constraints on the interpretation of our number theoretic vocabulary are inadequate. I then suggest that if we consider the manner in which the natural numbers figure in our computational practices – e.g. in characterizing how we compute sums and products or determine prime factorizations – it follows that our application of computational terms such as “computable function” and “tractable computational problem” indirectly uniquely determines their structure. (shrink)

It is shown that the elementary principles Count and Count are logically independent in the system IΔ0 of Bounded Arithmetic. More specifically it is shown that Count implies Count exactly when each prime factor in p is a factor in q.

The degree structure of functions induced by a polynomial-time reducibility first introduced in G. Miller's work on the complexity of prime factorization is investigated. Several basic results are established including the facts that the degrees restricted to the sets do not form an upper semilattice and there is a minimal degree, as well as density for the low degrees, a weak form of the exact pair theorem, the existence of minimal pairs and the decidability of the Π2 theory of (...) the low degrees. (shrink)

Use left and right arrow keys to move the gun left and right. You reduce a number by shooting it with its prime factors. Each time a prime factor hits a number, the number is divided by that factor. If the number is a prime number you can shoot it with a special "P" ("P" for "prime") missile which reduces it directly to 1. To fire a 2, 3, 5 or 7, just type the (...) corresponding key on the keyboard. To fire 11, 13, 17 or 19, type the first letter of the number (in lower case), i.e. "e" for 11, "t" for 13, "s" for 17 and "n" for 19. Type "p" (lower case) to fire the "P" missile. In all cases a number is "dead" when it is reduced to 1. If a number hits you, then you're dead. (shrink)

The system called F is essentially a sub-theory of Frege Arithmetic without the ad infinitum assumption that there is always a next number. In a series of papers (Systems for a Foundation of Arithmetic, True” Arithmetic Can Prove Its Own Consistency and Proving Quadratic Reciprocity) it was shown that F proves a large number of basic arithmetic truths, such as the Euclidean Algorithm, Unique Prime Factorization (i.e. the Fundamental Law of Arithmetic), and Quadratic Reciprocity, indeed a sizable amount of (...) arithmetic. In particular, F proves some (but not all) of the Peano Axioms; that is, F proves the axioms of a sub-theory - call it FPA - of second-order Peano-Arithmetic. This short technical note will demonstrate that the converse also holds, in the following sense. F has the same language as second-order Peano Arithmetic except that, in addition, it has a two-place predicate symbol “Μ”. Then it is possible to provide a definition, indeed a reasonable definition, for “Μ” such that FPA proves all the axioms of F. So F and FPA effectively have the same proof-theoretic strength. In particular FPA, which lacks the Successor Axiom stating that every natural number has a successor, is able to prove the Euclidean Algorithm, Unique Prime Factorization, and Quadratic Reciprocity, indeed (again) a sizable amount of arithmetic. (shrink)

ExcerptWhat factors lead to any war being fought in a particular manner? How and why do those factors become institutionalized, or abandoned, as prime forms of war for typifying other armed conflicts in changing world orders? When and why do the prevailing parameters of world order shape the conduct of war? Questions about the forms of war became highly salient in 1945 when, by virtue of the United Nations Charter, “the peoples of the United Nations determined” to organize stronger (...) institutions for global governance with an elaborate apparatus of multiple functional agencies “to save succeeding generations from the scourge of war” by establishing conditions “under which justice and respect for the obligations arising from treaties and other sources of international law can be maintained” as well as to “promote social progress and better standards of life in larger freedom.”1. (shrink)

This study examines executive perceptions of business information control. Specifically, the study explores (a) whether executives perceive certain types of information control being practiced within their businesses; and, (b) whether the executives regard such practices as ethical. In essence, the study suggests that both superiors and subordinates selectively practice information control. Even more importantly, however, executives see such practices as ethically acceptable on the part of superiors but as ethically questionable on the part of subordinates. A closer look at the (...) responding executives' profile characteristics – age, gender, education and salary – reveals the complexity of these perceptions. Most importantly, gender and age emerge as two prime factors influencing executive perceptions regarding both the practice and the ethics of information control. Suggestions for future research are included at the end of the article. (shrink)

In the present scenario of globalisation, knowledge has become the prime factor of production for competitive advantage. This calls for acquisition and utilisation of knowledge for innovation and technical change on a constant basis, which is only possible in a ‘learning organisation’. Innovative activities of a learning organisation are influenced by three main factors: (1) internal learning; (2) external learning; and (3) the innovation strategies decided upon by the enterprise management. An assumption has been made that, particularly in (...) developing countries, absorption and adaptation of technologies, i.e. indigenisation, take place through a process of ‘learning by doing’. Taking this into consideration, this paper focuses on a few case studies carried out at NISTADS, New Delhi, India, on small enterprises in the formal as well as traditional sectors, highlighting the learning process in an organisational context and how it brings in innovation and technological change at enterprise level. The study demonstrates that the learning environment in an organisational context is an indispensable process to be innovative and building up capabilities for technological change. This in turn also calls for strong networking of the enterprises with academia, R&D institutions and other enterprises, to create knowledge clusters. This builds up a strong case for a network approach of learning organisations not only at the regional level but also at the cross-cultural level for constant innovation and technical change. (shrink)

The prime and paramount factor that characterizes the Catholic philosopher is a respect for the Catholic philosophical tradition. To respect a person or a tradition is to see it as a bearer of value; respect does not automatically entail agreement. The Catholic philosophical tradition is not doctrinally unified, but is defined by a mutuality of involvement in a common project: that of developing a perspective that enables reason and religion to exist in a holistic unicity that fructifies each (...) through its interaction with the other. Catholic philosophers should respect their intellectual tradition because it is an important part of acquiring their identity as thinkers and persons. Three useful approaches to appropriating and respecting a tradition are: (1) restoration and revival; (2) preservation of issues by re-opening and re-examining its questions; and (3) revivification of its spirit. (shrink)

The aim of the present study was to investigate the effect of observing other’s movements on subsequent performance in bottlenose dolphins. The imitative ability of non-human animals has intrigued a number of researchers. So far, however, studies in dolphins have been confined to intentional imitation concerned with the explicit request to imitate other agents. In the absence of instruction to imitate, do dolphins (un)intentionally replicate other’s movement features? To test this, dolphins were filmed while reaching and touching a stimulus before (...) and after observing another dolphin (i.e., model) performing the same action. All videos were reviewed and segmented in order to extract the relevant movements. A marker was inserted post hoc via software on the videos upon the anatomical landmark of interest (i.e., rostrum) and was tracked throughout the time course of the movement sequence. The movement was analyzed using an in-house software developed to perform two-dimensional (2D) post hoc kinematic analysis. The results indicate that dolphins’ kinematics is sensitive to other’s movement features. Movements performed for the “visuomotor priming” condition were characterized by a kinematic pattern similar to that performed by the observed dolphin (i.e., model). Addressing the issue of spontaneous imitation in bottlenose dolphins might allow ascertaining whether the potential or impulse to produce an imitative action is generated, not just when they intend to imitate, but whenever they watch another conspecific’s behavior. In closing, this will clarify whether motor representational capacity is a by-product of factors specific to humans or whether more general characteristics such as processes of associative learning prompted by high level of encephalization could help to explain the evolution of this ability. (shrink)