Identities for the Widder transform and transforms with Bessel function kernels

In the present paper, we consider the classical Widder transform, the H_ν-transform, the K_ν-transform, and the Y_ν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms.     

A rational approximation based on Bernstein polynomials for high order initial and boundary values problems

We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ C^d+2[a, b].     

On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

Coverings and Ring-Groupoids

We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.     

Routing problems: A bibliography

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.     

Synthesis of heterocycles. Part II. New routes to acetylthiadiazolines and alkylazothiazoles

Methylglyoxalyl chloride arylhydrazones (III) react with an ethanolic solution of thiourea to give 2-amino-4-methyl-5-arylazothiazoles (XII) instead of the expected 2-acetyl-4-aryl-5-imino-Δ²-1,3,4-thiadiazolines (V) which were obtained from III and potassium thiocyanate. 3-Thiocyanato-2,4-pentanedione (IV) coupled with diazotized anilines to give V. The postulated routes to formation of V and XII from III are given. Nitrosation of V gave the corresponding N-nitroso derivatives (VI) which decomposed upon refluxing in dry xylene to give 2,4-disubstituted-Δ²-1,3,4-thiadiazolin-5-ones (VII). Boiling of either V or VI with hydrochloric acid gave the hydrochloride salt (VIII). The thiadiazolines V gave the respective N-acyl derivatives (IX) and (X) with acetic anhydride and benzoyl chloride in pyridine.     

Generating sets of finite singular transformation semigroups

J.M. Howie proved that $\operatorname {Sing}_{n}$ , the semigroup of all singular mappings of {1,…,n} into itself, is generated by its idempotents of defect 1 (in J. London Math. Soc. 41, 707–716, 1966). He also proved that if n≥3 then a minimal generating set for $\operatorname {Sing}_{n}$ contains n(n?1)/2 transformations of defect 1 (in Gomes and Howie, Math. Proc. Camb. Philos. Soc. 101. 395–403, 1987). In this paper we find necessary and sufficient conditions for any set for transformations of defect 1 in $\operatorname {Sing}_{n}$ to be a (minimal) generating set for $\operatorname {Sing}_{n}$ .     

Optimal production in a competitive market under yield uncertainty

Motivated by the U.S. influenza vaccine market, we study the impact of random yield and production capacity on the number of firms, total supply, consumer surplus and social welfare in a market with identical suppliers. We formulate a two-stage game with endogenous entry, where each entering firm aims to maximize its profit under yield uncertainty subject to a production capacity constraint. We show that if firms produce full capacity in the equilibrium, then there are fewer firms in the equilibrium compared to the social optimum even for small levels of yield uncertainty. Furthermore, we prove that if firms do not produce full capacity in the equilibrium, they will not produce full capacity in the social optimum.     

NEW DYNAMIC INEQUALITIES FOR DECREASING FUNCTIONS AND THEOREMS OF HIGHER INTEGRABILITY

In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, P′olya, D'Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.