Miracle-dz/UniFAR-FTUs huggingface dataset:
Temperature dependence of polarized photoluminescence from nonpolar m-plane InGaN multiple quantum wells for blue laser diodes

Polarized photoluminescence (PL) spectra from nonpolar m-plane InGaN multiple quantum wells (MQWs) in blue laser diode wafers fabricated on m-plane GaN substrates were measured as a function of temperature. The polarization ratio (ρ) and the energy difference between the highest and the second highest valence bands estimated from the energy difference between PL peaks (ΔE) increased with increasing InN molar fraction x (or the estimated anisotropic compressive strain along the m-axis eyy) in the MQWs. The values of ρ at 300K and ΔE were 0.71 and 76meV for the case of 430nm PL peak (x=0.104, eyy=+0.75%) and 0.92 and 123meV for the case of 485nm PL peak (x=0.175, eyy=+1.26%). These results suggest that the preferred stripe direction is the c axis for nonpolar m-plane laser diodes in the region from violet to near green.
Fractional Yamabe problem on locally flat conformal infinities of Poincare-Einstein manifolds

We study, in this paper, the fractional Yamabe problem introduced by Gonzalez-Qing on the conformal infinity (M^n, [h]) of a Poincare-Einstein manifold (X^{n+1}, g^{+}) with either n=2 or n> 3 and (M^n, [h]) is locally flat - namely (M, h) is locally conformally flat. However, as for the classical Yamabe problem, because of the involved quantization phenomena, the variational analysis of the fractional one exhibits also a local situation and a global one. Furthermore the latter global situation includes the case of conformal infinites of Poincare-Einstein manifolds of dimension either 2 or of dimension greater than 2 and which are locally flat. Hence the minimizing technique of Aubin-Schoen in that case clearly requires an analogue of the Positive Mass theorem of Schoen-Yau, which is not known to hold. Using the works of Caffarelli-Sylvestre, Chang-Gonzalez, Gonzalez-Qing and new, sharp estimates of the Caffarelli-Sylvestre extension of the fractional standard bubbles, which are derived via a suitable interaction interpretation of them rather than Fourier transform, combined with the algebraic topological argument of Bahri-Coron, we bypass the latter Positive Mass issue and show that any conformal infinity of a Poincar\'e-Einstein manifold of dimension either n=2 or of dimension n>2 and which is locally flat admits a Riemannian metric of constant fractional scalar curvature. As a byproduct of our arguments we derive new sharp expansions of the involved Poisson kernel and Green's functions near their singularities, hence answering the first part of the conjecture of Kim-Musso-Wei.
Comparison principle, stochastic completeness and half-space theorems

We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a comparison principle with geometric barriers for establishing mean curvature estimates for sto chastically complete submanifolds in Riemannian products, Riemannian submersions and wedges. These estimates are applied for obtaining both horizontal and vertical half-space theo rems for submanifolds in H n ×R l .
The computer study of transport processes under extreme conditions

A method is developed to investigate the behaviour of a liquid under the action of a very high shearing force using computer simulated molecular dynamics. Values for the viscosity are calculated but these require more extensive computation for statistical accuracy. A short calculation is, however, sufficient to establish the nature of the processes involved, and to plot the velocity distribution curve; these graphs are presented. The method abandons the usual homogeneous isotropic cyclic conditions used so far in calculation of transport coefficients and can be applied to arbitrarily large shear.
Complex Analysis of Real Functions III: Extended Fourier Theory

In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that the complete Fourier theory of integrable real functions is contained within that structure, that is, within the structure of the space of inner analytic functions on the open unit disk. We then extend the Fourier theory beyond the realm of integrable real functions, to include for example singular Schwartz distributions, and possibly other objects.
Nijenhuis forms on Lie-infinity algebras associated to Lie algebroids

ABSTRACT Introducing Nijenhuis forms on L∞-algebras gives a general frame to understand deformations of the latter. We give here a Nijenhuis interpretation of a deformation of an arbitrary Lie algebroid into an L∞-algebra. Then we show that Nijenhuis forms on L∞-algebras also give a short and eﬃcient manner to understand Poisson-Nijenhuis structures and, more generally, the so-called exact Poisson quasi-Nijenhuis structures with background.
Regularity bounds for complexes and their homology

Abstract Let R be a standard graded algebra over a field k. We prove an Auslander–Buchsbaum formula for the absolute Castelnuovo–Mumford regularity, extending important cases of previous works of Chardin and Römer. For a bounded complex of finitely generated graded R-modules L, we prove the equality reg L = maxi ∈ $_{\mathbb Z}$ {reg Hi (L) − i} given the condition depth Hi(L) ⩾ dim H i+1(L) - 1 for all i < sup L. As applications, we recover previous bounds on regularity of Tor due to Caviglia, Eisenbud–Huneke–Ulrich, among others. We also obtain strengthened results on regularity bounds for Ext and for the quotient by a linear form of a module.
Order of Starlikeness and Convexity of certain integral transforms using duality techniques

For $\alpha\geq 0$, $\beta 0, \quad \phi\in {\mathbb{R}},{\,}z\in {\mathbb{D}}; \end{align*} is taken into consideration. The Pascu class of $\xi$-convex functions of order $\sigma$ $(M(\sigma,{\,}\xi))$, having analytic characterization \begin{align*} {\rm Re\,}\frac{\xi z(zf'(z))'+(1-\xi)zf'(z)}{\xi zf'(z)+(1-\xi)f(z)}>\sigma,\quad 0\leq \sigma< 1,\quad z\in {\mathbb{D}}, \end{align*} unifies starlike and convex functions class of order $\sigma$. The admissible and sufficient conditions on $\lambda(t)$ are investigated so that the integral transforms \begin{align*} V_{\lambda}(f)(z)= \int_0^1 \lambda(t) \frac{f(tz)}{t} dt, \end{align*} maps the function from $\mathcal{W}_{\beta}(\alpha,\gamma)$ into $M(\sigma,{\,}\xi)$. Further several interesting applications, for specific choice of $\lambda(t)$ are discussed which are related to the classical integral transform.
Colossal dielectric behavior of semiconducting Sr2TiMnO6 ceramics

Manganitelike double perovskite Sr2TiMnO6 (STMO) ceramics fabricated from the powders synthesized via the solid-state reaction route, exhibited dielectric constants as high as similar to 10(5) in the low frequency range (100 Hz-10 kHz) at room temperature. The Maxwell-Wagner type of relaxation mechanism was found to be more appropriate to rationalize such high dielectric constant values akin to that observed in materials such as KxTiyNi(1-x-y)O and CaCu3Ti4O12. The dielectric measurements carried out on the samples with different thicknesses and electrode materials reflected the influence of extrinsic effects. The impedance studies (100 Hz-10 MHz) in the 180-300 K temperature range revealed the presence of two dielectric relaxations corresponding to the grain boundary and the electrode. The dielectric response of the grain boundary was found to be weakly dependent on the dc bias field (up to 11 V/cm). However, owing to the electrode polarization, the applied ac/dc field had significant effect on the low frequency dielectric response. At low temperatures (100-180 K), the dc conductivity of STMO followed a variable range hopping behavior. Above 180 K, it followed the Arrhenius behavior because of the thermally activated conduction process. The bulk conductivity relaxation owing to the localized hopping of charge carriers obeyed the typical universal dielectric response.
Multi-normed spaces

We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is analogous to, but distinct from, an existing theory of `operator spaces'; it is designed to relate to general spaces $L^p$ for $p\in [1,\infty]$, and in particular to $L^1$-spaces, rather than to $L^2$-spaces. After recalling in Chapter 1 some results in functional analysis, especially in Banach space, Hilbert space, Banach algebra, and Banach lattice theory that we shall use, we shall present in Chapter 2 our axiomatic definition of a `multi-normed space' $((E^n, \norm_n) : n\in \N)$, where $(E, \norm)$ is a normed space. Several different, equivalent, characterizations of multi-normed spaces are given, some involving the theory of tensor products; key examples of multi-norms are the minimum and maximum multi-norm based on a given space. Multi-norms measure `geometrical features' of normed spaces, in particular by considering their `rate of growth'. There is a strong connection between multi-normed spaces and the theory of absolutely summing operators. A substantial number of examples of multi-norms will be presented. Following the pattern of standard presentations of the foundations of functional analysis, we consider generalizations to `multi-topological linear spaces' through `multi-null sequences', and to `multi-bounded' linear operators, which are exactly the `multi-continuous' operators. We define a new Banach space ${\mathcal M}(E,F)$ of multi-bounded operators, and show that it generalizes well-known spaces, especially in the theory of Banach lattices. We conclude with a theory of `orthogonal decompositions' of a normed space with respect to a multi-norm, and apply this to construct a `multi-dual' space.
Finite-dimensional representations of difference operators, and the identification of remarkable matrices

Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers z_{n}, and of an arbitrary additional parameter (a respectively q), and provide finite-dimensional representations of the two operators acting on a function f(z) as follows: [f(z+a)-f(z)]/a respectively [f(qz)-f(z)]/[(q-1)z]. These representations are exact---in a sense explained in the paper---when the function f(z) is a polynomial in z of degree less than N. This formalism allows to transform difference equations valid in the space of polynomials of degree less than N into corresponding matrix-vector equations. As an application of this technique several remarkable square matrices of order N are identified, which feature explicitly N arbitrary numbers z_{n}, or the N zeros of polynomials belonging to the Askey and q-Askey schemes. Several of these findings have a Diophantine character.
Singular values of products of random matrices and polynomial ensembles

Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show how their result can be interpreted as a transformation of polynomial ensembles. We also show that the squared singular values of the product of M-1 complex Ginibre matrices with one truncated unitary matrix is a polynomial ensemble, and we derive a double integral representation for the correlation kernel associated with this ensemble. We use this to calculate the scaling limit at the hard edge, which turns out to be the same scaling limit as the one found by Kuijlaars and Zhang for the squared singular values of a product of M complex Ginibre matrices. Our final result is that these limiting kernels also appear as scaling limits for the biorthogonal ensembles of Borodin with parameter theta > 0, in case theta or 1/theta is an integer. This further supports the conjecture that these kernels have a universal character.
External branch lengths of $\Lambda $-coalescents without a dust component

$\Lambda$-coalescents model genealogies of samples of individuals from a large population by means of a family tree whose branches have lengths. The tree's leaves represent the individuals, and the lengths of the adjacent edges indicate the individuals' time durations up to some common ancestor. These edges are called external branches. We consider typical external branches under the broad assumption that the coalescent has no dust component, and maximal external branches under further regularity assumptions. As it transpires, the crucial characteristic is the coalescent's rate of decrease $\mu(b)$, $b\geq 2$. The magnitude of a typical external branch is asymptotically given by $n/\mu(n)$, where $n$ denotes the sample size. This result, in addition to the asymptotic independence of several typical external lengths hold in full generality, while convergence in distribution of the scaled external lengths requires that $\mu(n)$ is regularly varying at infinity. For the maximal lengths, we distinguish two cases. Firstly, we analyze a class of $\Lambda$-coalescents coming down from infinity and with regularly varying $\mu$. Here the scaled external lengths behave as the maximal values of $n$ i.i. d. random variables, and their limit is captured by a Poisson point process on the positive real line. Secondly, we turn to the Bolthausen-Sznitman coalescent, where the picture changes. Now the limiting behavior of the normalized external lengths is given by a Cox point process, which can be expressed by a randomly shifted Poisson point process.
The lift on a small sphere in a slow shear flow

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.
Integration on the Surreals: a Conjecture of Conway, Kruskal and Norton

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field No of surreal numbers containing the reals and the ordinals, as well as a vast array of less familiar numbers. A longstanding aim has been to develop analysis on No as a powerful extension of ordinary analysis on the reals. This entails finding a natural way of extending important functions f from the reals to the reals to functions f* from the surreals to the surreals, and naturally defining integration on the f*. The usual square root, log, and exp were naturally extended to No by Bach, Conway, Kruskal, and Norton, retaining their usual properties. Later Norton also proposed a treatment of integration, but Kruskal discovered it has flaws. In his recent survey [2, p. 438], Siegel characterizes the question of the existence of a reasonable definition of surreal integration as "perhaps the most important open problem in the theory of surreal numbers. " This paper addresses this and related unresolved issues with positive and negative results. In the positive direction, we show that semi-algebraic, semi-analytic, analytic, meromorphic, or more generally \'Ecalle-Borel transseriable functions extend naturally to No, and an integral with good properties exists on them. In the negative direction, we show there is a fundamental set-theoretic obstruction to naturally extending many larger families of functions.
Local and Global low-regularity solutions to the Generalized Leray-alpha equations

It has recently become common to study many different approximating equations of the Navier-Stokes equation. One of these is the Leray-$\alpha$ equation, which regularizes the Navier-Stokes equation by replacing (in most locations) the solution $u$ in the equation with $(1-\alpha^2\triangle)u$ the operator $(1-\alpha^2\triangle)$. Another is the generalized Navier-Stokes equation, which replaces the Laplacian with a Fourier multiplier with symbol of the form $|\xi|^\gamma$ ($\gamma=2$ is the standard Navier-Stokes equation), and recently in [14] Tao also considered multipliers of the form $|\xi|^\gamma/g(|\xi|)$, where $g$ is (essentially) a logarithm. The generalized Leray-$\alpha$ equation combines these two modifications by incorporating the regularizing term and replacing the Laplacians with more general Fourier multipliers, including allowing for $g$ terms similar to those used in [14]. Our goal in this paper is to obtain existence and uniqueness results with low regularity and/or non-$L^2$ initial data. We will also use energy estimates to extend some of these local existence results to global existence results.
Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal

We study theoretically the effect of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal. We consider irregularities such as misalignment of stripe position, deviation of intersecting angle, variation of layer thickness, and variation of stripe width. The results of our calculations show that misalignment of the stripes affects the width of the bandgap most. However, the photonic crystal is fairly robust to structural irregularities, so even with an irregularity of 15% the bandgap remains as large as 11%.
Lehmann–Suwa residues of codimension one holomorphic foliations and applications

Let $\mathcal{F}$ be a singular codimension one holomorphic foliation on a compact complex manifold $X$ of dimension at least three such that its singular set has codimension at least two. In this paper, we determine Lehmann-Suwa residues of $\mathcal{F}$ as multiples of complex numbers by integration currents along irreducible complex subvarieties of $X$. We then prove a formula that determines the Baum-Bott residue of simple almost Liouvillian foliations of codimension one, in terms of Lehmann-Suwa residues, generalizing a result of Marco Brunella. As an application, we give sufficient conditions for the existence of dicritical singularities of a singular real-analytic Levi-flat hypersurface $M\subset X$ tangent to $\mathcal{F}$.
Mourre's method for a dissipative form perturbation

We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutators method of Mourre. We also obtain the limiting absorption principle and uniform estimates for the derivatives of the resolvent. This abstract work is motivated by the Schr{o}dinger and wave equations on a wave guide with dissipation at the boundary.
Simultaneous prediction of toxicity of multiple chemicals to multiple species using multi‐dimensional functional relationships

A theoretical model is developed for the estimation of the toxicity of a large number of chemicals to a group of species for which the log‐toxicity values have strong linear relationships. The model is a multi‐dimensional functional relationship (FR) that allows for many missing values. It depends on an unobserved variate (denoted by ξ in the text), with a value for each chemical; for each species, the expectations of the log‐toxicity values are each linearly related to ξ. There are worthwhile gains in multi‐dimensional over the two‐dimensional FRs hitherto used. The model is applied to data on the toxicity of 51 chemicals to 10 species. It allows for species to have unequal variance about their expectations. There is good prediction of log‐toxicity from measurements on other species where only 30% of the combinations were measured even when the taxa are not closely related. Among the uses for this technique are (i) to predict toxicity for combinations of species and chemicals that have not been measured, (ii) to suggest a suitable range of concentrations for a new bioassay, (iii) identifying specificity, that is, chemicals that have a different relative toxicity for a particular species. Copyright © 2008 John Wiley & Sons, Ltd.
Recent anomalies in North Atlantic sea‐surface temperatures

Columbia University publishes a monthly compendium of global climatic data such as monthly pressure, land and sea-surface temperature and 500 mb height anomalies on its website (http://iridl.ldeo.columbia.edu/ maproom/.Global/). One aspect of recent months (summer and autumn 2004) is the large positive anomalies of sea-surface temperature around Iceland and Greenland, with temperatures up to 3 degC above the 1971–2000 reference period norm. Is this warmth a reality, and if so, how unusual is it? Also, bearing in mind that the typically vigorous winter westerly flow across the UK is in part attributable to temperature contrast across the Atlantic Ocean, does a warmer than normal northern Atlantic have any predictive value for the coming winter?
Standard-Model Bundles on Non-Simply Connected Calabi{Yau Threefolds

We give a proof of the existence of G = SU(5), stable holomorphic vector bundles on elliptically bered Calabi-Yau threefolds with fundamental group Z2. ThebundlesweconstructhaveEulercharacteristic3andananomalythatcanbe absorbed by M-theory ve-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group SU(3)CSU(2)LU(1)Y.
On the Cahn–Hilliard–Brinkman system

We consider a diffuse interface model for phase separation of an isothermal incompressible binary fluid in a Brinkman porous medium. The coupled system consists of a convective Cahn-Hilliard equation for the phase field $\phi$, i.e., the difference of the (relative) concentrations of the two phases, coupled with a modified Darcy equation proposed by H.C. Brinkman in 1947 for the fluid velocity $\mathbf{u}$. This equation incorporates a diffuse interface surface force proportional to $\phi \nabla \mu$, where $\mu$ is the so-called chemical potential. We analyze the well-posedness of the resulting Cahn-Hilliard-Brinkman (CHB) system for $(\phi,\mathbf{u})$. Then we establish the existence of a global attractor and the convergence of a given (weak) solution to a single equilibrium via {\L}ojasiewicz-Simon inequality. Furthermore, we study the behavior of the solutions as the viscosity goes to zero, that is, when the CHB system approaches the Cahn-Hilliard-Hele-Shaw (CHHS) system. We first prove the existence of a weak solution to the CHHS system as limit of CHB solutions. Then, in dimension two, we estimate the difference of the solutions to CHB and CHHS systems in terms of the viscosity constant appearing in CHB.
Orbital reducibility and a generalization of lambda symmetries

We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is investigated and employed to construct (orbitally) reducible systems. By standard identifications, the notions extend to non-autonomous ODEs of first and higher order. Moreover we thus obtain a generalization of the lambda symmetries of Muriel and Romero. Several examples are given.