Abel differential equations admitting a certain first integral

In this work algebro-geometric conditions to have a certain first integral for an Abel differential equation are given. These conditions establish a bridge with classical Galois theory because we transform the differential problem of finding a first integral for an Abel equation into an algebraic problem.     

改进的积分第一中值定理的应用

提供若干实例用以说明积分第一中值定理中的中值点ε∈[a，b]加强为ε∈（a，b）后所带来的好处．     

Lithium Salt of NH_2-substituted Graphene Nanoribbon with Twofold Donor-acceptor Framework: Large Nonlinear Optical Property

Based on graphene, a new class of second-order nonlinear optical(NLO) material, the lithium salt of NH2-substituted graphene nanoribbon with the twofold donor(D)/acceptor(A) mode, was reported. Eight stable 2Li-2NH2-GNR lithium salts, especially cis lithium salts, display considerably large β0 values. The combination of NH2-substituting and cis Li-doping makes β0 greatly increased from 0(GNR) to 1.2×105―2.9×105 a.u.(cis-2Li- 2NH2-GNRs). Our largest β0 value(2.9×105 a.u.) for cis-2Li-1,3-2NH2-AGNR is compara...     

Quantitative determination of oxybutynin hydrochloride by spectrophotometry, chemometry and HPTLC in presence of its degradation product and additives in different pharmaceutical dosage forms

Simple, accurate, sensitive and validated UV spectrophotometric, chemometric and HPTLC-densitometric methods were developed for determination of oxybutynin hydrochloride (OX) in presence of its degradation product and additives in its pharmaceutical formulations. Method A is the first derivative of ratio spectra (DD¹) which allows the determination of OX in presence of its degradate in pure form and tablets by measuring the peaks amplitude at 216 nm. Method B and C are principal component regression (PCR) and partial least-squares (PLS) for determination of OX in presence of its degradate in pure form, tablets and syrup. While, the developed high performance thin layer chromatography HPTLC-densitometric method was based on the separation of OX from its degradation product, methylparaben and propylparaben followed by densitometric measurement at 220 nm which allows the determination of OX in pure form, tablets and syrup. The separation was achieved using HPTLC silica gel F₂₅₄ plates and chloroform:methanol:ammonia solution:triethylamine (100:3:0.5:0.2, v/v/v/v) as the developing system. The accuracy, precision and linearity ranges of the developed methods were determined. The results obtained were statistically compared with each other and to that of a reported HPLC method, and there was no significant difference between the proposed methods and the reported method regarding both accuracy and precision.     

Multilayers in a modulated stochastic game

We are concerned with an antagonistic stochastic game between two players A and B which finds applications in economics and warfare. The actions of the players are manifested by a series of strikes of random magnitudes at random times exerted by each player against his opponent. Each of the assaults inflicts a random damage to enemy's vital areas. In contrast with traditional games, in our setting, each player can endure multiple strikes before perishing. Predicting the ruin time (exit) of player A, along with the total amount of casualties to both players at the exit is a main objective of this work. In contrast to the time sensitive analysis (earlier developed to refine the information on the game) we insert auxiliary control levels, which both players will cross in due game before the ruin of A. This gives A (and also B) an additional opportunity to reevaluate his strategy and change the course of the game. We formalize such a game and also allow the real time information about the game to be randomly delayed. The delayed exit time, cumulative casualties to both players, and prior crossings are all obtained in a closed-form joint functional.     

Projective background of the infinitesimal rigidity of frameworks

We present proofs of two classical theorems. The first one, due to Darboux and Sauer, states that infinitesimal rigidity is a projective invariant; the second one establishes relations (infinitesimal Pogorelov maps) between the infinitesimal motions of a Euclidean framework and of its hyperbolic and spherical images. The arguments use the static formulation of infinitesimal rigidity. The duality between statics and kinematics is established through the principles of virtual work. A geometric approach to statics, due essentially to Grassmann, makes both theorems straightforward. Besides, it provides a simple derivation of the formulas both for the Darboux-Sauer correspondence and for the infinitesimal Pogorelov maps. The research for this article was supported by the DFG Research Unit “Polyhedral Surfaces”.     

Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.     

The Upper Envelope of Positive Self-Similar Markov Processes

We establish integral tests in connection with laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation and on the study of the upper envelope of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100, [1995]). Research supported by a grant from CONACYT (Mexico).     

Fluctuation Identities Applied to the Hitting Time of a Half-line in the Plane

We study asymptotic estimates that contain the hitting time and the hitting place of a half-line by a two-dimensional random walk. Fluctuation identities are used without resorting to pair annihilation but by interchanging summation and integration. The same method applies to the hitting of the half-space by a one-dimensional random walk. The author was supported by a grant (no. 18740053) of Japan Society for the Promotion of Science.