The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

A totally ordered group G is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G{±∞}. Continuing work in Belegradek et al. 1115) and Point and Wagner 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. (...) Any pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property ); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions. (shrink)

An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function f (...) is a McNaughton function, i.e., f is continuous, piecewise linear, and each piece has integer coefficients. Conversely, McNaughton proved that all McNaughton functions f: [0,1] n →[0,1] are in Free n . The elements of Free n are logical equivalence classes of n-variable formulas in the infinite-valued calculus of Łukasiewicz. The aim of this paper is to provide an alternative, representation-free, characterization of Free n. (shrink)

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups (...) introduced in Belegradek et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

An explicit expression of the “Wigner operator” is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.

A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r $\epsilon$ R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations (...) and functions in M. We show that these quantifier elimination results essentially characterize the ordered modules M with finite indices of the submodules rM. It is proven that (1) any semi-bounded k-ary relation on M is equal, outside a finite union of k-strips, to a k-ary relation quantifier-free definable in M, (2) any semibounded function from $M^{k}$ to M is equal, outside a finite union of k-strips, to a piecewise linear function, and (3) any semi-bounded in M endomorphism of the additive group of M is of the form x $\mapsto \sigmax$ , for some $\mapsto \sigma$ from the field of fractions of R. (shrink)

Group size is a function of relative neocortical volume in nonhuman primates. Extrapolation from this regression equation yields a predicted group size for modern humans very similar to that of certain hunter-gatherer and traditional horticulturalist societies. Groups of similar size are also found in other large-scale forms of contemporary and historical society. Among primates, the cohesion of groups is maintained by social grooming; the time devoted to social grooming is linearly related to group size among the Old World (...) monkeys and apes. To maintain the stability of the large groups characteristic of humans by grooming alone would place intolerable demands on time budgets. It is suggested that (1) the evolution of large groups in the human lineage depended on the development of a more efficient method for time-sharing the processes of social bonding and that (2) language uniquely fulfills this requirement. Data on the size of conversational and other small interacting groups of humans are in line with the predictions for the relative efficiency of conversation compared to grooming as a bonding process. Analysis of a sample of human conversations shows that about 60% of time is spent gossiping about relationships and personal experiences. It is suggested that language evolved to allow individuals to learn about the behavioural characteristics of other group members more rapidly than is possible by direct observation alone. (shrink)

In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the n-dimensional vector space ℚn which contain n linearly independent elements. Thus the collection of torsion-free abelian groups (...) of rank at most n can be naturally identified with the set S of all nontrivial additive subgroups of ℚn. In 1937, Baer [4] solved the classification problem for the class Sof rank 1 groups as follows.Let ℙ be the set of primes. If G is a torsion-free abelian group and 0 ≠ x ϵ G, then the p-height of x is defined to behx = sup{n ϵ ℕ ∣ There exists y ϵ G such that pny = x} ϵ ℕ ∪{∞}; and the characteristic χ of x is defined to be the function. (shrink)

Dept. of Philosophy Center for Biomedical Center for Biomedical Dept. of Philosophy Carnegie Mellon Univ.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

In this book, we present a study of linear models and algorithms to find the optimal solution for them using the concepts of neuroscientific science. We know that the linear programming method is one of the important methods of operations research, the science that was the product of the great scientific development that our contemporary world is witnessing. The name operations research is given to the group of scientific methods used. In analyzing problems and searching for optimal solutions, (...) it is a science whose applications have achieved widespread success in various fields of life. What is meant by neutrosophic models are models in which the data are neutrosophic values, that is, variables such as in the objective function, which expresses profit if the model is a maximization model, and expresses a cost if the model is a minimization model, which in turn is affected by environmental conditions. (shrink)

Let equation image denote the inverse limit of all finite cyclic groups. Let F, G and H be abelian groups with H ≤ G. Let FβH denote the abelian group , where +βis defined by +β = + β — β) for a certain β : F → G linear mod H meaning that β = 0 and β + β — β ∈ H for all a, b in F. In this paper we show that the (...) following hold: The additive group of any nonstandard model ℤ* of the ring ℤ is isomorphic to βH for a certain β : ℤ*+/H → equation image linear mod H. equation image is isomorphic to βH for some β : equation image/H →ℚ linear mod H, though equation image is not the additive group of any model of Th and the exact sequence H → equation image → equation image/H is not splitting. (shrink)

We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

Reproductive division of labor has been proposed to play a key role for evolutionary transitions in individuality (ETIs). This chapter provides a guide to a theoretical model that addresses the role of a tradeoff between life-history traits in selecting for a reproductive division of labor during the transition from unicellular to multicellular organisms. In particular, it focuses on the five key assumptions of the model, namely (1) fitness is viability times fecundity; (2) collective traits are linear functions of (...) their cellular counterparts; (3) there is a tradeoff between cell viability and fecundity; (4) cell contribution to the collective is optimal; and (5) there is an initial reproductive cost in large collectives. Thereafter the chapter contrasts two interpretations of the model in the context of ETIs. Originally, the model was interpreted as showing that during the transition to multicellularity the fitness of the lower-level (the cells) is “transferred” to the higher level (the collective). Despite its apparent intuitiveness, fitness transfer may obscure actual mechanisms in metaphorical language. Thus, an alternative and more conservative interpretation of the model that focuses on cell traits and the evolutionary constraints that link them is advocated. In addition, it allows for pursuing subsequent questions, such as the evolution of development. (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

Aim: Participation in classroom physical activity breaks may improve children’s cognition, but few studies have involved adolescents. The primary aim of this study was to examine the effects of classroom-based resistance training with and without cognitive training on adolescents’ cognitive function.Methods: Participants were 97 secondary school students. Four-year 10 classes from one school were included in this four-arm cluster randomized controlled trial. Classes were randomly assigned to the following groups: sedentary control with no cognitive training, sedentary with cognitive training, (...) resistance training without cognitive training, and resistance training with cognitive training. Sessions varied in levels of both cognitive demand and resistance training and were administered three times per week for 4 weeks. Inhibition, cognitive flexibility, episodic memory, on-task behavior, and muscular fitness were assessed at baseline and post-test. Linear mixed models were used to examine changes within and between groups.Results: In comparison with the control group, episodic memory improved significantly in the resistance training without cognitive training group. There were no group-by-time effects for inhibition or cognitive flexibility. Classroom activity breaks both with and without cognitive demand improved participants’ on-task behavior in comparison with the control and sedentary group. The resistance training programs did not lead to improvements in muscular fitness.Conclusion: Participation in body weight resistance training without cognitive training led to selective improvements in episodic memory. No training effects were found for inhibition or cognitive flexibility. A longer study period may be necessary to induce improvements in muscular fitness and associated changes in inhibition and cognitive flexibility.Clinical Trial Registration:https://www.anzctr.org.au/ACTRN12621001341819.aspx, Australian New Zealand Clinical Trials Registry—ACTRN12621001341819. (shrink)

This study aims to examine the neural correlates of cognitive shifting during the Dimensional Change Card Sort Task task with functional near-infrared spectroscopy. Altogether 49 children completed the DCCS tasks, and 25 children passing all items were classified into the Switch group. Twenty children committing more than one perseverative errors were grouped into the Perseverate group. The Switch group had Brodmann Area 9 and 10 activated in the pre-switch period and BA 6, 9, 10, 40, and 44 in the post-switch (...) period. In contrast, the Perseverate group had BA 9 and 10 activated in the pre-switch period and BA 8, 9, 10 in the post-switch period. The general linear model results afford strong support to the “V-shape curve” hypothesis by identifying a significant decrease–increase cycle in BA 9 and 44, the neural correlations of cognitive shifting. (shrink)

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic (...) behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied. (shrink)

BackgroundExercise is one of the effective ways to improve cognition. Different forms of exercises, such as aerobic exercise, resistance exercise, and coordination exercise, have different effects on the improvement of cognitive impairment. In recent years, exergames based on Non-Immersive Virtual Reality have been widely used in entertainment and have gradually been applied to clinical rehabilitation. However, the mechanism of NIVR-Exergames on improving motor cognition has not been clarified. Therefore, the aim of this study is to find whether NIVR-Exergames result in (...) a better neural response mechanism to improve the area of the cerebral cortex related to motor cognition under functional near-infrared spectroscopy dynamic monitoring in comparison with resistance exercise.MethodsA cross-over study design was adopted in this study, and 15 healthy young subjects were randomly divided into group A and group B according to a computerized digital table method. Task 1 was an NIVR-Exergame task, and Task 2 was resistance band stretching. Group A first performed Task 1, rested for 30 min, and then performed Task 2. Group B had the reverse order. The fNIRS test was synchronized in real time during exercise tasks, and heart rate measurements, blood pressure measurements, and 2-back task synchronization fNIRS tests were performed at baseline, Post-task 1, and Post-task 2. The primary outcomes were beta values from the general linear model in different regions of interest, and the secondary outcomes were heart rate, blood pressure, reaction time of 2-back, and accuracy rate of 2-back.ResultsThe activation differences of Task 1 and Task 2 in the right premotor cortex and the left PMC were statistically significant. There were statistically significant differences in the activation of the right supplementary motor area, left dorsolateral prefrontal cortex, left and right PMC between baseline and Post-task 1. The differences in systolic pressure between the two groups at three time points among women were statistically significant.ConclusionIn this study, we found that NIVR-Exergames combined with motor and challenging cognitive tasks can promote the activation of SMA, PMC and DLPFC in healthy young people compared with resistance exercise alone, providing compelling preliminary evidence of the power for the rehabilitation of motor and cognitive function in patients with central nervous system diseases. (shrink)

A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von Neumann–Morgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

Background and objectives: Developmental coordination disorder is a neurodevelopmental motor disorder occurring in 5-6% of school-aged children. It is suggested that children with DCD show deficits in motor learning. Transcranial direct current stimulation enhances motor learning in adults and children but is unstudied in DCD. We aimed to investigate if tDCS, paired with motor skill training, facilitates motor learning in a pediatric sample with DCD.Methods: Twenty-eight children with diagnosed DCD were randomized and placed into a treatment or sham group. Anodal (...) tDCS was applied in conjunction with fine manual training over 5 consecutive days. Children's motor functioning was assessed with the Purdue Pegboard Test and Jebsen-Taylor Hand Function Test at baseline, post-intervention and 6 weeks following intervention. Group differences in rates of motor learning and skill transfer/retention were examined using linear mixed modeling and repeated measures ANOVAs, respectively.Results: There were no serious adverse events or drop-outs and procedures were well-tolerated. Independent of group, all participants demonstrated improved motor scores over the 5 training days [F, p < 0.001, 95% CI ], with no skill decay observed at retention. There was no interaction between intervention group and day [F, p = 0.086, 95% CI ].Conclusion: Children with DCD demonstrate motor learning with long-term retention of acquired skill. Motor cortex tDCS did not enhance motor learning as seen in other populations. Before conclusions of tDCS efficacy can be drawn, additional carefully designed trials with reproducible results are required.Clinical Trial Registration:ClinicalTrials.gov: NCT03453983. (shrink)

PurposeTo investigate spontaneous brain activity in patients with dry eye and healthy control using the fractional amplitude of low frequency fluctuation technique with the aim of elucidating the relationship between the clinical symptoms of DE and changes in brain function.Material and MethodsA total of 28 patients with DE and 28 matched healthy volunteers were enrolled. Resting-state functional magnetic resonance imaging scans were performed in both groups. Then all subjects were required to complete a comprehensive Hospital Anxiety and Depression Scale. (...) Receiver operating characteristic curve analysis was used to evaluate the differences in fALFF values between the two groups and their diagnostic value. Linear correlations between HADS and fALFF values in different brain regions of DE patients were analyzed using the Pearson correlation coefficient.ResultsPatients with DE had significantly higher fALFF values in the left calcarine sulcus than the HC group, while fALFF values in the bilateral middle frontal gyrus and right MFG/right inferior frontal gyrus were significantly lower in DE patients than in HC group. fALFF values had a high diagnostic value for differentiating patients with DE from the HC group. Right MFG and right MFG/IFG were significantly correlated with HADS values.ConclusionOur study found that DE mainly involved functional disorders in the brain areas of the left CS, bilateral MFG and right MFG/right IFG, which helped us to find possible clinical features of DE disease and reflected the potential pathological mechanism of DE. (shrink)

Hydrogen activation on the (100) surface of MoS2 structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of hydrogen; that is, an H2 molecule dissociates on an MoS2 catalyst surface into two hydrogen atoms, which react further with the catalyst surface under formation of either one Mo-H and one S-H (heterolytic) (...) or of two S-H surface groups (homolytic). Our results favor the heterolytic adsorption of hydrogen. Ni- and Co-promoted MoS2 have been considered to investigate the secondary promotional effect on the H2 dissociation. The authors observed a negative secondary promotional influence on the H2 dissociation in the case of Ni-promoted MoS2, whereas Co shows a positive effect. (shrink)

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.

Proper linear models are those in which predictor variables are given weights such that the resulting linear composite optimally predicts some criterion of interest; examples of proper linear models are standard regression analysis, discriminant function analysis, and ridge regression analysis. Research summarized in P. Meehl's book on clinical vs statistical prediction and research stimulated in part by that book indicate that when a numerical criterion variable is to be predicted from numerical predictor variables, proper linear models (...) outperform clinical intuition. Improper linear models are those in which the weights of the predictor variables are obtained by some nonoptimal method. The present article presents evidence that even such improper linear models are superior to clinical intuition when predicting a numerical criterion from numerical predictors. In fact, unit weighting is quite robust for making such predictions. The application of unit weights to decide what bullet the Denver Police Department should use is described; some technical, psychological, and ethical resistances to using linear models in making social decisions are considered; and arguments that could weaken these resistances are presented. (shrink)

The productivity of (human) information processing as an economic activity is a question that is raising some interest. Using Marschak's evaluation framework, Radner and Stiglitz have shown that, under certain conditions, the production function of this activity has increasing marginal returns in its initial stage. This paper shows that, under slightly different conditions, this information processing function has repeated convexities with ongoing processing activity. Even for smooth changes in the signals' likelihoods, the function is only piecewise smooth with non-differentiable (...) convexities at points of conditional changes of action. For linear likelihood functions the processing value proves to be piecewise linear with convexities at these levels. (shrink)

Which groups are isomorphic to automorphism groups of models of Peano Arithmetic? It will be shown here that any group that has half a chance of being isomorphic to the automorphism group of some model of Peano Arithmetic actually is.For any structure, let Aut() be its automorphism group. There are groups which are not isomorphic to any model= (N, +, ·, 0, 1, ≤) of PA. For example, it is clear that Aut(N), being a subgroup of Aut((, (...) <)), must be torsion-free. However, as will be proved in this paper,if(A, <)is a linearly ordered set and G is a subgroup of Aut((A, <)),then there are modelsofPAsuch that Aut() ≅G.Ifis a structure, then its automorphism group can be considered as a topological group by letting the stabilizers of finite subsets ofAbe the basic open subgroups. If′ is an expansion of, then Aut(′) is a closed subgroup of Aut(). Conversely, for any closed subgroupG≤ Aut() there is an expansion′ ofsuch that Aut(′) =G. Thus, ifis a model of PA, then Aut() is not only a subgroup of Aut((N, <)), but it is even aclosedsubgroup of Aut((N, ′)).There is a characterization, due to Cohn [2] and to Conrad [3], of those groupsGwhich are isomorphic to closed subgroups of automorphism groups of linearly ordered sets. (shrink)

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in absolutely ubiquitous structures from classical logic.

Formal and social epistemologists have devoted significant attention to the question of how to aggregate the credences of a group of agents who disagree about the probabilities of events. Moss and Pettigrew argue that group credences can be a linear mean of the credences of each individual in the group. By contrast, I argue that if the epistemic value of a credence function is determined solely by its accuracy, then we should, where possible, aggregate the underlying statistical models that (...) individuals use to generate their credence functions, using “stacking” techniques from statistics and machine learning first developed by Wolpert. (shrink)

BackgroundSarcomas are a diverse group of neoplasms that vary greatly in clinical presentation and responsiveness to treatment. Given the differences in the sites of involvement, rarity, and treatment modality, a multidisciplinary approach is required. Previous literature suggests patients with sarcoma suffer from poorer quality of life especially physical and functional wellbeing. Adolescent and young adult patients are an underrepresented population in cancer research and have differing factors influencing QoL.MethodsRetrospective analysis of Young Adult patients enrolled in the Sarcoma Tissue Repository at (...) University of Iowa. QoL was assessed using the self-report FACT-G questionnaire at enrollment and 12 months post-diagnosis; overall scores and the 4 wellbeing subscales were calculated. Linear mixed effects models were used to measure the association between the rate of change in FACT-G subscale scores and baseline clinical, comorbidity, and treatment characteristics.Results49 patients were identified. 57.1% of patients had a malignancy involving an extremity. Mean FACT-G scores of overall wellbeing improved from baseline to 12 months. Social and emotional wellbeing did not differ significantly between baseline and 12 months. Physical wellbeing and functional wellbeing scores improved from baseline to 12 months. No difference was seen for FACT-G overall scores for age, sex, laterality, marital status, performance status, having children, clinical stage, limb surgery, chemotherapy, or tumor size. A difference was demonstrated in physical wellbeing scores for patients with baseline limitation compared to those with no baseline limitation. A difference was demonstrated in social wellbeing based on anatomical site.ConclusionYoung adults with sarcoma treated at a tertiary center had improvements in overall reported QoL at 12 months from diagnosis. Overall baseline QoL scores on FACT-G were lower than the general adult population for YA patients with sarcoma but at 12 months became in line with general population norms. The improvements seen merit further investigation to evaluate how these change over the continuum of care. Quality of life changes may be useful outcomes of interest in sarcoma trials. (shrink)

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *ℤ of the ring ℤ of integers by using a linear mod 1 function h : F ℚ, where F is the α-dimensional vector space over ℚ when α is the cardinality of *ℤ. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.

Self-efficacy is an important predictor of learning and achievement. By definition, self-efficacy requires a task-specific assessment, in which students are asked to evaluate whether they can solve concrete tasks. An underlying assumption in previous research into such assessments was that self-efficacy is a one-dimensional construct. However, empirical evidence for this assumption is lacking, and research on students’ performance suggests that it depends on various task characteristics. The present study explores the potential multi-dimensionality of self-efficacy in the topic of linear (...) functions. More specifically, we investigate how three task characteristics – the representational format, embedding in a real-life context, or the required operation – are related to students’ self-efficacy. We asked 8th and 9th graders to evaluate their self-efficacy on specific linear function tasks which systematically varied along the three dimensions of task characteristics. Using confirmatory factor analysis, we found that a two-dimensional model which includes the task characteristic of real-life context fitted the data better than other two-dimensional models or a one-dimensional model. These results suggest that self-efficacy with linear functions is empirically separable with respect to tasks with vs. without a real-life context. This means that in their self-evaluation of linear function tasks students particularly rely on whether or not the linear function task is embedded in a real-life context. This study highlights the fact that even within a specific content domain students’ self-efficacy can be considered a multi-dimensional construct. (shrink)

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their *-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.

Let $\scr{M}=\langle M,+,<,0,S\rangle $ be a linear o-minimal expansion of an ordered group, and $G=\langle G,\oplus ,e_{G}\rangle $ an n-dimensional group definable in $\scr{M}$ . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ${\ssf V}\text{-definable}$ subgroup U of $\langle M^{n},+\rangle $ and a lattice L of rank equal to the dimension of the 'compact part' of G.

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ( $$IP_{3}$$ ) and adenosine triphosphate (ATP) in various cells including pancreatic $$\beta$$ -cells. The calcium signaling mechanisms regulating $$IP_{3}$$, ATP and insulin responsible for various functions of $$\beta$$ -cells are still not well understood. Any disturbance in these mechanisms can alter the functions of $$\beta$$ -cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation (...) for calcium dynamics and a system of first-order differential equations for $$IP_{3}$$, ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of $$IP_{3}$$ -production and degradation, ATP production and insulin secretion on calcium dynamics in a $$\beta$$ -cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of $$IP_{3}$$, ATP and insulin levels in a $$\beta$$ -cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of $$IP_{3}$$, ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in $$IP_3$$, ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases. (shrink)

We review the mathematical theory ofSL(n, R) and its double-covering group $\overline {SL} (n,R)$ , especially forn = 2, 3, 4. After discussing a variety of physical applications, we show that $\overline {SL} (3,R)$ provides holonomic curved space (“world”) spinors with an infinite number of components. We construct the relevant holonomic “manifield” and discuss the gravitational interaction of a proton as an example.

Mitigation is a pragmatic-linguistic category traditionally related to the theory of verbal politeness. Previous work on this issue has shown that conversational hedging is largely conditioned by the speaker’s identity (Albelda 2012, Cestero 2011, Samper 2017), that is why a deeper understanding of attenuating phenomena requires close attention to the social context underpinning communicative interactions. This paper advances some preliminary results from the ongoing research on discursive mitigation in the Malaga-PRESEEA spoken corpus. The analysis is centered on the underlying mitigating (...) functions in the speech performance of a group of speakers with university education. Since one of our main objectives is contrastive, and previous solid research on attenuation has been carried out within the PRESEEA context, its methodological basis has been assumed (Albelda 2012, Cestero 2011, Samper 2017). Results of multifactorial logistic regression analysis from our data are partially similar to those obtained in previous studies: mitigation formulas are frequent among the well-educated speakers we have studied, especially those related to self-protection functions. Women—more than men—, and younger speakers—more than every other age-group—, tend to lead this use. (shrink)

Mitigation is a pragmatic-linguistic category traditionally related to the theory of verbal politeness. Previous work on this issue has shown that conversational hedging is largely conditioned by the speaker’s identity (Albelda 2012, Cestero 2011, Samper 2017), that is why a deeper understanding of attenuating phenomena requires close attention to the social context underpinning communicative interactions. This paper advances some preliminary results from the ongoing research on discursive mitigation in the Malaga-PRESEEA spoken corpus. The analysis is centered on the underlying mitigating (...) functions in the speech performance of a group of speakers with university education. Since one of our main objectives is contrastive, and previous solid research on attenuation has been carried out within the PRESEEA context, its methodological basis has been assumed (Albelda 2012, Cestero 2011, Samper 2017). Results of multifactorial logistic regression analysis from our data are partially similar to those obtained in previous studies: mitigation formulas are frequent among the well-educated speakers we have studied, especially those related to self-protection functions. Women—more than men—, and younger speakers—more than every other age-group—, tend to lead this use. (shrink)