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We describe two distinct simple, short and self contained proofs of the composition lemma.
Let the finite distributive lattice $D$ be isomorphic to the congruence lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that correspond to principal congruences under this isomorphism. Then $Q$ contains $0,1 \in D$ and…
This note presents a simple approach to proving the interlacing properties of positive zeros of Bessel functions of the first kind. The approach relies only on the standard recurrence relations between Bessel functions and characterising…
Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
In this paper we assemble some results about the upper-semicontinuity and lower-semicontinuity of the feasible correspondence and the solution correspondence of linear programming problems allowing variability of all parameters of such…
We develop a model where firms determine the price at which they sell their differentiable goods, the volume that they produce, and the inputs (types and amounts) that they purchase from other firms. A steady-state production network…
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…
Let C subset Reg be a non-empty class (of regular cardinal). Then the logic L(Q^{cf}_C) has additional nice properties: it has homogeneous model existence property.
There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting…
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling…
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition,…
A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…