Poincaré duality in P.A. Smith theory

Let , or more generally be a finite -group, where is an odd prime. If acts on a space whose cohomology ring fulfills Poincaré duality (with appropriate coefficients ), we prove a mod congruence between the total Betti number of and a number which depends only on the -module structure of . This improves the well known mod congruences that hold for actions on general spaces.

     

Signed Fuzzy-Valued Measures and Radon-Nikodym Theorem of Fuzzy-Valued Measurable Functions

In this paper, we introduce and study the signed fuzzy-valued measure and using the representation theorem of fuzzy numbers, we establish the Radon-Nikodym theorem for fuzzy-valued measurable functions with respect to fuzzy-valued measures.AMS Subject Classification (2000): 28E10, 04A72The research of this work is supposed by a grant of the education committee of Liaoning Province, China #20161049     

The tame kernel of imaginary quadratic fields with class number 2 or 3

This paper presents improved bounds for the norms of exceptional finite places of the group , where is an imaginary quadratic field of class number 2 or 3. As an application we show that .

     

Another Note on the Greatest Prime Factors of Fermat Numbers

For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if F_m = 2^2m + 1 is the mth Fermat number, then P(F_m) 2^m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(F_a,m), where F_a,m = a^2m + 1 whenever a is even and m a¹⁸.AMS Subject Classification (1991) 11A51 11J86     

On the Number of Lost Customers in Stationary Loss Systems in the Light Traffic Case

For the stationary loss systems M/M/m/K and GI/M/m/K, we study two quantities: the number of lost customers during the time interval (0,t] (the first system only), and the number of lost customers among the first n customers to arrive (both systems). We derive explicit bounds for the total variation distances between the distributions of these quantities and compound Poisson–geometric distributions. The bounds are small in the light traffic case, i.e., when the loss of a customer is a rare event. To prove our results, we show that the studied quantities can be interpreted as accumulated rewards of stationary renewal reward processes, embedded into the queue length process or the process of queue lengths immediately before arrivals of new customers, and apply general results by Erhardsson on compound Poisson approximation for renewal reward processes.     

The Bargmann-Wigner formalism for spin 2 fields

The Bargmann-Wigner formalism has been applied to describe the spin-2 field in terms of the symmetric fourth-rank multi-Dirac spinor Ψ_αβγδ. A serious problem of the standard anzatz is that the resulting equation of motion has the trivial solution with all field components being independently equal to zero. We here show that this problem is an artefact of the neglection of terms containing the matrix γ⁵ in the decomposition of ϕ into the Clifford algebra basis. We further emphasize importance of the gauge 4-vector field in that respect.     

The Dedekind-Mertens lemma and the contents of polynomials

Let be a commutative ring, let be an indeterminate, and let . There has been much recent work concerned with determining the Dedekind-Mertens number =min , especially on determining when = . In this note we introduce a universal Dedekind-Mertens number , which takes into account the fact that deg() + for any ring containing as a subring, and show that behaves more predictably than .

     

3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem

We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka–Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only if it is flat.     

A Discussion on Particle Number and Quantum Indistinguishability

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schr?dinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. Graciela Domenech — Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).     

Density,viscosity, conductance,and transference number of concentrated aqueous magnesium chloride at 25°C

The density, viscosity, conductance, and transference number of aqueous magnesium chloride at 298.15°K are reported for the concentration range 0 to 5.7m. The transference numbers were determined using the emf method. It was found that the viscosity, conductance, and transference number of aqueous magnesium chloride are similar to those for aqueous nickel chloride. It was therefore tentatively concluded that incomplete dissociation and complex formation was unlikely to be of importance in nickel chloride solutions.