Field redefinitions at string 1-loop order are often required by supersymmetry, for instance in order to make the Kähler structure of the scalar kinetic terms manifest. We derive the general structure of the field redefinitions and the Kähler potential at string 1-loop order in a certain class of string theory models (4-dimensional toroidal type IIB orientifolds with ${\cal N}=1$ supersymmetry) and for a certain subsector of fields (untwisted Kähler moduli and the 4-dimensional dilaton). To do so we make use of supersymmetry, perturbative axionic shift symmetries and a particular ansatz for the form of the 1-loop corrections to the metric on the moduli space. Our results also show which terms in the low-energy effective action have to be calculated via concrete string amplitudes in order to fix the values of the coefficients (in the field redefinitions and the Kähler potential) that are left undetermined by our general analysis based on (super)symmetry.

In this paper, we study the stability and instability of the ground states for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential (for short, INLS$_c$ equation): $$iu_{t} +\Delta u+c|x|^{-2}u+|x|^{-b} |u|^{\sigma } u=0,\; u(0)=u_{0}(x) \in H^{1},\;(t,x)\in \mathbb R\times\mathbb R^{d},$$ where $d\ge3$, $0

This paper discusses the enumeration for the total number of all rooted spanning forests of the labeled complete tripartite graph. We enumerate the total number by a combinatorial decomposition.

We evaluate string one-loop contributions to the Einstein-Hilbert term in toroidal minimally supersymmetric type IIB orientifolds with D-branes. These have potential applications to the determination of quantum corrections to the moduli Kahler metric in these models.

The possibility of carbohydrate separation in BEH HILIC (Ethylene Bridged Hybride, Hydrophilic Interaction Liquid Chromatography) column was studied by ultra-performance liquid chromatography (UPLC) with evaporative light scattering detector (ELSD) and mobile phase containing amine compounds as modifiers. The chromatography conditions and ELSD parameters were optimized to separate five typical carbohydrates and applied to analysis of four infant milk powders. The linear ranges of carbohydrate determination were 20-300mg/L for fructose and glucose, 20-250mg/L for sucrose and lactose, and 35-180mg/L for fructo-oligosaccharide. The LODs were 16.4mg/L for fructose and glucose, 17.3mg/L for sucrose, 20.0mg/L for lactose, and 46.7mg/L for fructo-oligosaccharide. Relative standard deviations (RSDs) ranged between 3.45-4.23%, 1.46-4.17%, 4.14-5.60%, 1.39-4.09%, and 2.49-3.61% for fructose, glucose, sucrose, lactose, and fructo-oilgosaccharide, respectively and recoveries ranged between 95.0 and 105.4%

We present an alternative one-electron equation for resolving many-electron problem to one-electron approximation and including the exchange and correlation effects in an analytical way, thereby fulfilling the requirements for ab initio calculation. To derive one-electron equation, we accept a new notion of equivalent function suggestive of the pseudo wavefunction. As a result, we reduce many-electron equation to one-electron including the exchange effect in an analytical method. Moreover we accept the notion of phase norm for two electrons to resolve the electronic correlation problem. The phase norm is used to specify the electron-approachable limit between particles. We take into consideration the electronic correlation with the help of a correlation-hole function in terms of the phase norm, by which multiplying the integrand of the operator term representing the interaction between electrons. Using the phase norm leads to analytical consideration of the electronic correlation without employing in a factitious way the additional term pertaining to correlation, so it embodies the physical essence of electronic correlation. The derived equation becomes an one-electron equation which does not include an additional term pertaining to the exchange and correlation, but takes into consideration the exchange and correlation effects in a rigorous ab initio way.

In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function with both local self-similarity and uncertainty is necessary. In this paper, we propose a construction of fuzzy valued recurrent fractal interpolation function using recurrent iterated function system that interpolates the given data set of fuzzy numbers. And we show some properties of the constructed fuzzy valued RFIFs: Holder continuity and stability of the interpolation function due to perturbations in the data set or the vertical scaling factors.

In this paper, we study the stability and instability of the ground states for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential (for short, INLS$_c$ equation): $$iu_{t} +\Delta u+c|x|^{-2}u+|x|^{-b} |u|^{\sigma } u=0,\; u(0)=u_{0}(x) \in H^{1},\;(t,x)\in \mathbb R\times\mathbb R^{d},$$ where $d\ge3$, $0

In this paper we study some dynamical properties such as Frequent Hypercyclicity Criterion, chaos, disjoint hypercyclicity and F-transitivity via Furstenberg family F for generalized bilateral weighted shift operator on the standard Hilbert C-module over C-algebra of compact operators on a separable Hilbert space.

We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a ``superposition'' model, which leads to an asymptotic power-law distribution of the number of occurrences (or frequency) of words, that is, Zipf's law. The model is well consistent with observations.

In this paper we investigated the point-wise time-space estimates of the fundamental solution for higher order Schrödinger equation. These estimates improve the result of Yao [2] and generalize the one of Cui [1].

We use the truncated-unity functional renormalization group (TUFRG) to study many-body instabilities of correlated electrons in graphene doped near the van Hove singularity (VHS). The system is described by an extended Hubbard model including several Coulomb repulsions between neighboring sites. With the repulsion parameters, which turn out to be suitable for low-energy consideration of graphene, we find a spin-bond-order phase in the vicinity of the VHS. This phase gives way to a spin-density-wave phase when involving a weak additional screening. The ground-state phase diagram is presented in the space of the doping level and the screening parameter. We describe in detail both of these spin-ordered states by using recently developed TUFRG + MF scheme, i.e., a combined approach of TUFRG and mean-field (MF) theory. The collinear states are energetically preferable in both cases of the spin bond order and the spin-density wave. But if the third-nearest-neighbor hopping is absent, these spin orders become chiral. The band structures of two collinear spin-ordered states are presented, revealing the metallic behavior of the system.

An incline is an additively idempotent semiring in which the product of two elements is always less than or equal to either factor. This paper proves that the only regular inclines are distributive lattices, which also implies that there is no noncommutative regular incline.

In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal interpolation functions that interpolate a given data set of fuzzy numbers using an iterated function system and study the Holder continuity of the constructed function. Firstly, we construct an iterated function system (IFS) using the given data set and construct a fuzzy-valued fractal interpolation function whose graph is the attractor of the constructed IFS. Next, we find the relationship between the fuzzy-valued fractal interpolation function and the fractal interpolation function of the level set of the data set. Finally, we prove the Holder continuity of the fuzzy-valued fractal interpolation function.

In this paper, we consider black-box multiobjective optimization problems in which all objective functions are not given analytically. In multiobjective optimization, it is important to produce a set of uniformly distributed discrete solutions over the Pareto front to build a good approximation. In black-box biobjective optimization, one can evaluate distances between solutions with the ordering property of the Pareto front. These distances allow to be able to evaluate distribution of all solution points, so it is not difficult to maintain uniformity of solutions distribution. However, problems with more than two objectives do not have ordering property, so it is noted that these problems require other techniques to measure the coverage and maintain uniformity of solutions distribution. In this paper, we propose an algorithm based on a trust region method for the Pareto front approximation in black-box multiobjective optimization. In the algorithm, we select a reference point in the set of non-dominated points by employing the density function and explore area around this point. This ensures uniformity of solutions distribution even for problems with more than two objective functions. We also prove that the iteration points of the algorithm converge to Pareto critical points. Finally, we present numerical results suggesting that the algorithm generates the set of well-distributed solutions approximating the Pareto front, even in the case for the problems with three objective functions.

In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distribution is derived. And as their applications, pricing formulae of savings plans that provide a choice of indexing and discrete geometric average Asian options are derived and the fact that the price of discrete geometric average Asian option converges to the price of continuous geometric average Asian option when the largest distance between neighboring monitoring times goes to zero is proved.

We analytically and numerically investigate magneto-plasmons in metal films surrounded by a ferromagnetic dielectric. In such waveguide using a metal film with a thickness exceeding the Skin depth, an external magnetic field in the transverse direction can induce a significant spatial asymmetry of mode distribution. Superposition of the odd and the even asymmetric modes over a distance leads to a concentration of the energy on one interface which is switched to the other interface by the magnetic field reversal. The requested magnitude of magnetization is exponentially reduced with the increase of the metal film thickness. Based on this phenomenon, we propose a waveguide-integrated magnetically controlled switchable plasmonic routers with 99-%-high contrast within the optical bandwidth of tens of THz. This configuration can also operate as a magneto-plasmonic modulator.

We study the solution to Kolmogorov-Feller equation and by using it provide pricing formulas of well known some options under jump-diffusion model.

Earth rotation is one of astronomical phenomena without which it is impossible to think of human life. That is why the investigation on the Earth rotation is very important and it has a long history of study. Invention of quartz clocks in the 1930s and atomic time 1950s and introduction of modern technology into astronomic observation in recent years resulted in rapid development of the study in Earth's rotation. The theory of the Earth rotation, however, has not been up to the high level of astronomic observation due to limitation of the time such as impossibility of quantitative calculation of moment of external force for Euler's dynamical equation based on Newtoniam mechanics. As a typical example, we can take the problems that cover the instabilities of the Earth's rotation proved completely by the astronomic observations as well as polar motion, the precession and nutation of the Earth rotation axis which have not been described in a single equation in a quantitative way from the unique law of the Earth rotation. In particular, at present the problem of what the main factor causing the instabilities of the Earth rotation is has not been solved clearly in quantitative ways yet. Therefore, this paper addresses a quantitative proof that the main factor which causes the instabilities of the Earth rotation is the moment of external force rather than variations in the relative atmospheric angular momentum and in moment of inertia of the Earth's body due to the time limitation and under some assumptions. Then the future direction of research is proposed.