Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Functionalized Silver-Ion-Mediated α-dC/β-dC Hybrid Base Pairs with Exceptional Stability: α-d-5-Iodo-2′-Deoxycytidine and Its Octadiynyl Derivative in Metal DNA

Silver-mediated α-dC–Ag⁺–β-dC hybrid base pairs decorated with 5-iodo- or 5-octadiynyl residues are well accommodated in duplex DNA. A strong T_m increase and favorable thermodynamic data for duplex DNA were observed after addition of silver ions. The phenomenon is particularly obvious when both nucleobases of the base pairs are functionalized. Neither the position of the base pair, nor the type of 5-substituent had a negative influence. On the contrary, functionalization of conventional silver-mediated β-dC–Ag⁺–β-dC homo base pairs showed a negative impact induced by the bulky substituents. To this end, cytosine modified 12-mer oligodeoxynucleotides were prepared by solid-phase synthesis employing new α-anomeric 2′-deoxycytidine phosphoramidites. A multigram scale synthesis was developed for 5-iodo-α-d -2′-deoxycytidine ( 1 ) employing the direct glycosylation of cytosine with Hoffer's α-d -halogenose followed by separation of anomeric DMT nucleosides. Regarding base-pair stability and functionalization silver-mediated α/β-dC hybrid base pairs were found to be superior to β/β-dC homo pairs. According to their extraordinary properties, they might find applications in DNA diagnostics, material science, or nanotechnology.     

Certificateless signature and proxy signature schemes from bilinear pairings

Due to avoiding the inherent escrow of identity-based cryptography and yet not requiring certificates to guarantee the authenticity of public keys, certificateless public key cryptography has received a significant attention. Due to various applications of bilinear pairings in cryptography, numerous pairing-based encryption schemes, signature schemes, and other cryptographic primitives have been proposed. In this paper, a new certificateless signature scheme based on bilinear pairings is presented. The signing algorithm of the proposed scheme is very simple and does not require any pairing computation. Combining our signature scheme with certificateless public key cryptography yields a complete solution of certificateless public key system. As an application of the proposed signature scheme, a certificateless proxy signature scheme is also presented. We analyze both schemes from security point of view.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 95–103, January–March, 2005.     

高温超导体Josephson阵列在磁场中的微波响应与磁通涡旋激发

本文从分析相变电阻率 ρP 和磁通蠕动电阻率 ρF 出发 ,指出当T小于某一温度T0 时 ,ρF>ρP,而当T >T0 时 ,ρF 远小于 ρP,并进一步分析了 ρF 与 ρP 随温度的变化率分布图 ,得出磁通蠕动电阻率 ρF 随温度的变化率分布图跟微波响应曲线具有相似的分布特征 ,结果表明 :高温超导体的非平衡微波响应机制可能与磁通涡旋的激发有关 .     

Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor

Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.

     

Exceptional Θ-Correspondences I

Let G be either a split SO(2n+2), or a split adjoint group of type En, (n=6,7,8), over a p-adic field. In this article we study correspondences arising by restricting the minimal representation of G to various dual pairs in G.     

The π-π-theorem for manifold pairs with boundaries

The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L _*(π ₁(Y) → π ₁(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π ₁(X) ? π ₁(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP _* for manifold pairs and splitting obstruction groups LS _*. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds.     

Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.     

Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources.     

Exceptional set of a representation with fractional powers

We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x ^c] + [p ^c], where x is a natural number and p is a prime.