A major limitation in triple-helix formation arises from the weak energy of interaction between the third strand and the double-stranded target. We tried to increase the stacking interaction contribution within the third strand by extending the aromatic domain of thymine. We report here the use of 2,4-quinazolinedione as a substitute for thymine in the canonical TA*T triplet. The synthesis and ...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

It has been argued that a particular type of quantum-vacuum variable $q$ can provide solution to the main cosmological constant problem and possibly also give cold-dark-matter component. We now show same field may suggest new interpretation big bang, namely as quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by equilibrium values $q=\ifmmode\p...

In this paper we construct transitive t-designs from the linear groups L(2, q), q ≤ 23. Thereby we classify t-designs, t ≥ 2, admitting a transitive action of the linear groups L(2, q), q ≤ 23, up to 35 points and obtained numerous transitive designs, for 36 ≤ v ≤ 55. In many cases we proved the existence of t-designs with certain parameter sets. Among others we constructed t-designs with param...

We study the initial value problem for integrable nonlocal nonlinear Schr\"odinger (NNLS) equation \[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 \] with symmetric boundary conditions: $q(x,t)\to Ae^{2iA^2t}$ as $x\to\pm\infty$, where $A>0$ is an arbitrary constant. describe asymptotic stage of modulation instability NNLS by computing large-time asymptotics solution $q(x,t)$ this proble...

An accurate theoretical description of the dynamic properties correlated quantum many-body systems, such as structure factor S(q, ω), is important in many fields. Unfortunately, highly Monte Carlo methods are usually restricted to imaginary time domain, and analytic continuation imaginary-time density–density correlation function F(q, τ) real frequencies a notoriously hard problem. Here, it arg...

This paper deals with p-Laplacian systems ut − div(|∇u|p−2∇u) = ∫ Ωv α(x, t)dx, x ∈Ω, t > 0, vt − div(|∇v|q−2∇v) = ∫ Ωu β(x, t)dx, x ∈ Ω, t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN , where p,q ≥ 2, α,β ≥ 1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow ...

Let G be a bounded domain in R" and Q = G X (0, T). We consider the solution^«) of the pseudo-parabolic initial-value problem (1 + M(x))y,(u) + L(x)y(u) = u in L2(Q), y(-,0;u) = 0 in L2(G), to be the state corresponding to the control u. Here M(x) and L{x) are symmetric uniformly strongly elliptic second-order partial differential operators. The control problem is to find a control un in a fixe...

Title of dissertation: ASYMPTOTIC PROBLEMS FOR STOCHASTIC PROCESSES WITH REFLECTION AND RELATED PDE’s Konstantinos Spiliopoulos, Doctor of Philosophy, 2009 Dissertation directed by: Professor Mark I. Freidlin Department of Mathematics Asymptotic problems for stochastic processes with reflection and for related partial differential equations (PDE’s) are considered in this thesis. The stochastic ...