Template design based on molecular and crystal structure similarity to regulate conformational polymorphism nucleation: the case of α,ω-alkanedicarboxylic acids

Template design on polymorph control, especially conformational polymorphs, is still in its infancy and the result of polymorph control is often accidental. A method of regulating the crystallization of conformational polymorphs based on the crystal structure similarity of templates and the target crystal form has been developed. Crystal structure similarity was considered to be able to introduce lattice matching (geometric term) with chemical interactions to regulate conformational polymorph nucleation. The method was successfully applied to induce the crystallization of DA7-II [HOOC–(CH2) n −2–COOH (diacids), named DAn, where n = 7, 9, 15, 17 and II represents the metastable polymorph] on the surface of DA15-II. An analogous two-dimensional plane – the (002) face of both DA15-II and DA7-II – was firstly predicted as the epitaxially attached face with similar lattice parameters and the strongest adsorption energy. The powder DA15-II template with the preferred orientation face in (002) presented much stronger inducing DA7-II ability than the template with other preferred orientation faces. The epitaxial growth of DA7-II on DA15-II through an identical (002) face was clearly observed and verified by the single-crystal inducing experiments. The molecular dynamics simulation results demonstrated that the strong interactions occurred between DA7 molecules and the (002) face of DA15-II. This method has been verified and further applied to the crystallization of DA7-II on the surface of DA17-II and DA9-II on the surface of DA15-II. This study developed a strategy based on structure similarity to regulate the conformational polymorph and verified the significant role of lattice matching and chemical effects on the design and preparation of templates.

Wormhole models in R2-gravity for f(R, T) theory with a hybrid shape function

In the present paper, we explore wormholes in R²-gravity within the f(R,T) formalism by using b(r)= re^r0-r (hybrid shape function). The functional form f(R, T)= R + αR² +λT is considered with R and T as the Ricci scalar and trace of energy-momentum tensor, respectively, α and β are controlling parameters. With the help of the EoS, ω= \frac{p_r}{\rho}, geometric behavior is analyzed and energy conditions are discussed in anisotropic scenario. In this investigation, significant contribution of the quadratic geometric term (R²) and linear trace term (T) are shown for validating energy conditions for specific shape function and analyzing wormhole solutions in absence of exotic matter. Also, we observe that the energy conditions are valid in whole range (r ≥ r0) in the case of constant redshift function with this shape function.

THE INVARIANT MEASURE OF RANDOM WALKS IN THE QUARTER-PLANE: REPRESENTATION IN GEOMETRIC TERMS

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative.

Parametric Stability of a Nonlinear Rotating Blade

The stability of period-1 motions of a rotating blade with geometric nonlinearity is studied. The roles of cubic stiffening geometric term are considered in the study of nonlinear periodic motions and its stability and bifurcations of a rotating blade. The nonlinear model of a rotating blade is reduced to the ordinary differential equations through the Galerkin method, and the gyroscopic systems with parametric excitations are obtained. The generalized harmonic balance method is employed to determine the period-1 solutions and the corresponding stability and bifurcations.

Geometric Asymptotic Approximation of Value Functions

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.

ON EFFECTIVE F-THEORY ACTION IN TYPE IIA COMPACTIFICATIONS

Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of space–time vanishes, we also prove a version of the Kriz–Sati conjecture by extending the arguments of Diaconescu–Moore–Witten. We also briefly discuss why even this special case allows interesting examples.

Variational Problems in Image Segmentation and I-Convergance Methods

Variational models for image segmentation aim to recover a piecewise smooth approximation of a given input image together with a discontinuity set which represents the boundaries of the segmentation. In particular, the variational method introduced by Mumford and Shah includes the length of the discontinuity boundaries in the energy. Because of the presence of such a geometric term, the minimization of the corresponding functional is a difficult numerical problem. We consider a mathematical framework for the Mumford-Shah functional and we discuss the computational issue. We suggest the use of the G-convergence theory to approximate the functional by elliptic functionals which are convenient for the purpose of numerical computation. We then discuss the design of an iterative numerical scheme for image segmentation based on the G-convergent approximation. The relation between the Mumford-Shah model and the

(e, 2 e)-Spectroscopy and the Electronic Structure of Molecules. A Short Review with Selected Examples

The simple plane wave target Hartree-Fock impulse approximation for the (e, 2e) reaction is developed. One result of the approximation is the separation of the expression for the (e, 2e) cross-section into a kinematic factor and a structure factor that contains all of the information about the target. When the target is a molecule, the structure factor can be further separated into atomic terms and a geometric term. This is illustrated for a simple one-electron homonuclear diatomic molecule. Three examples of the application of (e, 2e) spectroscopy to systems of chemical interest are given. They are borazine (inorganic benzene), the methyl siloxanes and the inorganic complex trimethylamine boron trifluoride.