Strengthening of the Kneser theorem on zeros of solutions of the equation <Emphasis Type=Italic>u</Emphasis>″ + <Emphasis Type=Italic>q</Emphasis>(<Emphasis Type=Italic>t</Emphasis>)<Emphasis Type=Italic>u</Emphasis> = 0 using one functional equation

We present conditions under which a linear homogeneous second-order equation is nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.     

On the asymptotic optimality of the <Emphasis Type=Italic>cμ</Emphasis>/<Emphasis Type=Italic>θ</Emphasis> rule under ergodic cost

We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served. For class i, service is provided at rate μ _i , and abandonment occurs at rate θ _i . In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c _i μ _i /θ _i asymptotically minimizes an ergodic holding cost, where c _i denotes the equivalent holding cost per unit time for class i.     

Calibration relations for <Emphasis Type=Italic>B</Emphasis><Subscript><Emphasis Type=Italic>φ</Emphasis></Subscript>-splines of fourth order

We study necessary and sufficient conditions for the smoothness of (not necessarily polynomial) splines of fourth order. We establish the uniqueness of a space of splines of maximal smoothness and prove embeddings on refined grids. We also obtain the corresponding calibration relations. Bibliography: 12 titles.     

A finite-difference method for the numerical solution of the Schrödinger equation

A new approach, which is based on a new property of phase-lag for computing eigenvalues of Schrödinger equations with potentials, is developed in this paper. We investigate two cases: (i) The specific case in which the potential V(x) is an even function with respect to x. It is assumed, also, that the wave functions tend to zero for x → ±∞. (ii) The general case of the Morse potential and of the Woods-Saxon or optical potential. Numerical and theoretical results show that this new approach is more efficient compared to previously derived methods.     

Upper bounds for the first dirichlet eigenvalue of a tube around an algebraic complex curve of ℂ<Emphasis Type=Italic>P</Emphasis><Superscript><Emphasis Type=Italic>n</Emphasis></Superscript>(<Emphasis Type=Italic>λ</Emphasis>)

We give an upper bound for the first Dirichlet eigenvalue of a tube around a complex curve P of ℂP ⁿ (λ) which depends only on the radius of the tube and the degrees of the polynomials defining P. The bound is sharp on a totally geodesic ℂP ¹(λ) and gives a gap between the eigenvalue of a tube around ℂP ¹(λ) and around other complex curves.     

Sur la rigidité des groupes de triangles (<Emphasis Type=Italic>r</Emphasis>, <Emphasis Type=Italic>p</Emphasis>, <Emphasis Type=Italic>q</Emphasis>)

We show the length spectral rigidity for the family of fuchsian triangular groups.     

On the basis property of eigenelements of ordinary linear differential operators in a space of the type <Emphasis Type=Italic>L</Emphasis><Subscript><Emphasis Type=Italic>p</Emphasis></Subscript>, <Emphasis Type=Italic>p</Emphasis> ≥ 2

For a linear differential expression with matrix coefficients in the class L _p , p ≥ 2, and with a parameter λ, we consider a boundary value problem with boundary conditions at the endpoints of the interval [a, b]. Under the condition that the problem is regular, we obtain a formula for the Fourier series expansion of an arbitrary vector function of the class L _p in the root functions of the problem.     

<Emphasis Type=Italic>Eω</Emphasis>-Clifford congruences and <Emphasis Type=Italic>Eω</Emphasis>-<Emphasis Type=Italic>E</Emphasis>-reflexive congruences on an inverse semigroup

This paper enlarges the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower T and lower K. Two classes of inverse semigroups, namely Eω-Clifford semigroups and Eω-E-reflexive semigroups, are studied. ((ω _T ) _K ) _T and (((ω _T ) _K ) _T ) _K are found to be the least Eω-Clifford and Eω-E-reflexive congruences on S, respectively. Characterizations of the congruences ((ω _T ) _K ) _T and (((ω _T ) _K ) _T ) _K are developed. The lattices of all Eω-Clifford and Eω-E-reflexive congruences are also studied.     

Generating <Emphasis Type=Italic>Sym</Emphasis>(<Emphasis Type=Italic>ω</Emphasis>) by Permutations Preserving Dense Orders

We show how generic permutations of ω can be presented by products of permutations preserving dense orders.     

New criteria for <Emphasis Type=Italic>λ</Emphasis>-Koszul algebras

The main purpose of this paper is to provide some new criteria for a standard graded algebra A = ⊕ _i≥0 A _i to be a λ-Koszul algebra, which was first introduced in [12] and was another class of “Koszul-type” algebras including Koszul and d-Koszul algebras as special examples.     

On the identification <Emphasis Type=Italic>H</Emphasis> = <Emphasis Type=Italic>H</Emphasis>′ in the Lions theorem and a related inaccuracy

We show that the common identification of H with its dual space in the famous functional frame V ⊂ H = H′ ⊂ V′ is incompatible with the distributional frame for some standard pdes and we recall an error related to this unnecessary identification which is repeated from years.     

Renormalization group and the <Emphasis Type=Italic>ɛ</Emphasis>-expansion: Representation of the <Emphasis Type=Italic>β</Emphasis>-function and anomalous dimensions by nonsingular integrals

In the framework of the renormalization group and the ɛ-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in ɛ. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ ³ model in the order ɛ ⁴ .