Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games

Inspired by Kalai-Samet [4] and Tijs [11], weighted average lexicographic values are introduced for share sets and for cores of cooperative games using induction arguments. Continuity properties and monotonicity properties of these weighted lexicographic values are studied. For subclasses of games (convex games, simplex games, big boss games) relations are established with weighted (exact) Shapley values.Cooperative games;average lexicographic value;weighted Shapley value

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

State determination: an iterative algorithm

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.Comment: 11 pages 3 figure

Observation of a nanophase segregation in LiCl aqueous solutions from Transient Grating Experiments

Transient Grating experiments performed on supercooled LiCl, RH2O solutions with R>6 reveal the existence of a strong, short time, extra signal which superposes to the normal signal observed for the R=6 solution and other glass forming systems. This extra signal shows up below 190 K, its shape and the associated timescale depend only on temperature, while its intensity increases with R. We show that the origin of this signal is a phase separation between clusters with a low solute concentration and the remaining, more concentrated, solution. Our analysis demonstrates that these clusters have a nanometer size and a composition which are rather temperature independent, while increasing R simply increases the number of these clusters.Comment: 19 pages+ 8 figures+ 2 table

Share Opportunity Sets and Cooperative Games

In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem.Cooperative games related to such share sets are introduced, which may be helpful in solving share problems.Relations between properties of share sets and properties of games are investigated.The average lexicographic value for share sets and for cooperative games is studied.cooperative games;bankruptcy games;average lexicographic value;opportunity sets

The Relationship between Teachers’ Measures of Resilience and Self-efficacy with their Intent to Remain in the Teaching Profession.

The study examined MDCPS teachers’ measure of resiliency and self-efficacy and their intention to remain in the teaching profession. A survey was sent to 2,000 MDCPS teachers who work within schools located in the Central Region. The survey consisted of the Teachers’ Sense of Self-Efficacy Scale, the Teacher Resiliency Survey, and the Intent to Stay Scale. Demographics information, teaching assignment, preservice preparation program, and Title I school status questions were part of the survey to account for them as control variables. The survey concluded with questions regarding the COVID-19 pandemic. An ordinary least-squares regression analysis was used to predict the value of teachers’ intent to stay. The data on teacher resiliency were inconsistent when compared with the findings of the other data. Teacher-reported resiliency levels were extremely low when compared to the reported levels of self-efficacy and intent to stay. Four different regression models were run, two with the teacher resiliency variable and two without. The first regression model examined teachers’ intent to remain in the teaching profession with teacher resiliency as part of the variables. The results showed three variables with statistical significance: Teacher Self-Efficacy Scale (p=.004), teachers’ age (p=.020) and Title I school status (p= .045). The second model examined the relationship of teachers’ intent to remain in MDCPS with teacher resiliency as part of the variables. The results revealed two variables with statistical significance: Teacher Self-Efficacy Scale (p= .010) and teachers who work at K8 Centers (p=.007). The third regression model examined teachers’ intent to remain in the teaching profession without teacher resiliency as part of the variables. The results indicated three variables with statistical significance: Teacher Self-Efficacy Scale (p=.002), teachers’ age (p=.023) and working in a high school (p= .034). The fourth model examined the relationship of teachers’ intent to remain in MDCPS without teacher resiliency as part of the variables. The results revealed two variables with statistical significance: Teacher Self-Efficacy Scale (p= .008) and teachers who work at K8 Centers (p=.005)