Charged Schrodinger Black Holes

We construct charged and rotating asymptotically Schrodinger black hole solutions of IIB supergravity. We begin by obtaining a closed-form expression for the null Melvin twist of a broad class of type IIB backgrounds, including solutions of minimal five-dimensional gauged supergravity, and identify the resulting five-dimensional effective action. We use these results to demonstrate that the near-horizon physics and thermodynamics of asymptotically Schrodinger black holes obtained in this way are essentially inherited from their AdS progenitors, and verify that they admit zero-temperature extremal limits with AdS_2 near-horizon geometries. Notably, the AdS_2 radius is parametrically larger than that of the asymptotic Schrodinger space.Comment: 22 pages, LaTe

Alien Registration- Brown, Max (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/25704/thumbnail.jp

INVESTIGATION OF HOW ENDOPLASMIC RETICULUM STRESS CAUSES INSULIN RESISTANCE AND NEUROINFLAMMATION

Endoplasmic reticulum (ER) stress is caused by the accumulation of mis/unfolded proteins in the ER. ER stress signalling pathways termed the unfolded protein response are employed to alleviate ER stress through increasing the folding capacity and decreasing the folding demand of the ER as well as removing mis/unfolded proteins. However, ER stress signalling pathways induce diverse cellular changes beyond changes to the ER. This study aims to further investigate some of these ER stress-mediated events. ER stress can cause activation of JNK. Prolonged ER stress-mediated JNK activation is reported to promote apoptosis whilst both acute and long-lasting JNK activation is proposed to cause insulin resistance. To begin with it is reported in this thesis that acute ER stress-induced JNK activation, which is dependent on IRE1α and TRAF2, promotes survival. In contrast to other studies, this thesis provides evidence that acute ER stress-mediated JNK activation does not inhibit insulin signalling during ER stress in several cell lines. However, prolonged ER stress, in four different cell lines, does inhibit insulin signalling in a JNK independent manner. This study argues that ER-stress-induced insulin resistance during prolonged ER stress involves inhibition of trafficking of newly synthesised insulin receptors through the secretory pathway to the plasma membrane. Finally ER stress can activate inflammatory signalling pathways other than JNK and thus ER stress may promote inflammation. Neuroinflammation and ER stress are reported in Parkinson’s disease (PD) yet a link between them has so far not been investigated. Using a cellular model of PD, it is reported in this thesis that ER stress has the potential to activate neuroinflammation in PD

Index Numbers of South Dakota Farm Prices

During the last generation, index numbers have gradually gone into general use among economists, statisticians, and business men. Because a farmer is a business man, it is important that he know what the trend of farm prices have been in the past and what the current trend is, so that he may anticipate changes which statistical analysis show are taking place in his particular phase of business.The Main objective of this study is to revise the existing South Dakota Farm Price Index. In order to furnish a comparable background for the presentation of these results it was found desirable (1) to review briefly the history and methods of collecting farm prices, (2) to review the more common methods of constructing farm prices index numbers, and (3) to review in detail the procedure used in constructing the existing index in order that an easy reference may be available for those who may desire to make use of it

Well-Distributed Sequences: Number Theory, Optimal Transport, and Potential Theory

The purpose of this dissertation will be to examine various ways of measuring how uniformly distributed a sequence of points on compact manifolds and finite combinatorial graphs can be, providing bounds and novel explicit algorithms to pick extremely uniform points, as well as connecting disparate branches of mathematics such as Number Theory and Optimal Transport. Chapter 1 sets the stage by introducing some of the fundamental ideas and results that will be used consistently throughout the thesis: we develop and establish Weyl\u27s Theorem, the definition of discrepancy, LeVeque\u27s Inequality, the Erdős-Turán Inequality, Koksma-Hlawka Inequality, and Schmidt\u27s Theorem about Irregularities of Distribution. Chapter 2 introduces the Monge-Kantorovich transport problem with special emphasis on the Benamou-Brenier Formula (from 2000) and Peyre\u27s inequality (from 2018). Chapter 3 explores Peyre\u27s Inequality in further depth, considering how specific bounds on the Wasserstein distance between a point measure and the uniform measure may be obtained using it, in particular in terms of the Green\u27s function of the Laplacian on a manifold. We also show how a smoothing procedure can be applied by propagating the heat equation on probability mass in order to get stronger bounds on transport distance using well-known properties of the heat equation. In Chapter 4, we turn to the primary question of the thesis: how to select points on a space which are as uniformly distributed as possible. We consider various diverse approaches one might attempt: an ergodic approach iterating functions with good mixing properties; a dyadic approach introduced in a 1975 theorem of Kakutani on proportional splittings on intervals; and a completely novel potential theoretic approach, assigning energy to point configurations and greedily minimizing the total potential arising from pair-wise point interactions. Such energy minimization questions are certainly not new, in the static setting--physicist Thomson posed the question of how to minimize the potential of electrons on a sphere as far back as 1904. However, a greedy approach to uniform distribution via energy minimization is novel, particularly through the lens of Wasserstein, and yields provably Wasserstein-optimal point sequences using the Green\u27s function of the Laplacian as our energy function on manifolds of dimension at least 3 (with dimension 2 losing at most a square root log factor from the optimal bound). We connect this to known results from Graham, Pausinger, and Proinov regarding best possible uniform bounds on the Wasserstein 2-distance of point sequences in the unit interval. We also present many open questions and conjectures on the optimal asymptotic bounds for total energy of point configurations and the growth of the total energy function as points are added, motivated by numerical investigations that display remarkably well-behaved qualities in the dynamical system induced by greedy minimization. In Chapter 5, we consider specific point sequences and bounds on the transport distance from the point measure they generate to the uniform measure. We provide provably optimal rates for the van der Corput sequence, the Kronecker sequence, regular grids and the measures induced by quadratic residues in a field of prime order. We also prove an upper bound for higher degree monomial residues in fields of prime order, and conjecture this to be optimal. In Chapter 6, we consider numerical integration error bounds over Lipschitz functions, asking how closely we can estimate the integral of a function by averaging its values at finitely many points. This is a rather classical question that was answered completely by Bakhalov in 1959 and has since become a standard example (`the easiest case which is perfectly understood\u27). Somewhat surprisingly perhaps, we show that the result is not sharp and improve it in two ways: by refining the function space and by proving that these results can be true uniformly along a subsequence. These bounds refine existing results that were widely considered to be optimal, and we show the intimate connection between transport distance and integration error. Our results are new even for the classical discrete grid. In Chapter 7, we study the case of finite graphs--we show that the fundamental question underlying this thesis can also be meaningfully posed on finite graphs where it leads to a fascinating combinatorial problem. We show that the philosophy introduced in Chapter 4 can be meaningfully adapted and obtain a potential-theoretic algorithm that produces such a sequence on graphs. We show that, using spectral techniques, we are able to obtain empirically strong bounds on the 1-Wasserstein distance between measures on subsets of vertices and the uniform measure, which for graphs of large diameter are much stronger than the trivial diameter bound

Dexterity analysis and robot hand design

Understanding about a dexterous robot hand's motion ranges is important to the precision grasping and precision manipulation. A planar robot hand is studied for object orientation, including ranges of motion, measures with respect to the palm, position reaching of a point in the grasped object, and rotation of the object about the reference point. The rotational dexterity index and dexterity chart are introduced and an analysis procedure is developed for calculating these quantities. A design procedure for determining the hand kinematic parameters based on a desired partial or complete dexterity chart is also developed. These procedures have been tested in detail for a planar robot hand with two 2- or 3-link fingers. The derived results are shown to be useful to performance evaluation, kinematic parameter design, and grasping motion planning for a planar robot hand

Improvement of modal scaling factors using mass additive technique

A general investigation into the improvement of modal scaling factors of an experimental modal model using additive technique is discussed. Data base required by the proposed method consists of an experimental modal model (a set of complex eigenvalues and eigenvectors) of the original structure and a corresponding set of complex eigenvalues of the mass-added structure. Three analytical methods,i.e., first order and second order perturbation methods, and local eigenvalue modification technique, are proposed to predict the improved modal scaling factors. Difficulties encountered in scaling closely spaced modes are discussed. Methods to compute the necessary rotational modal vectors at the mass additive points are also proposed to increase the accuracy of the analytical prediction

A new method to real-normalize measured complex modes

A time domain subspace iteration technique is presented to compute a set of normal modes from the measured complex modes. By using the proposed method, a large number of physical coordinates are reduced to a smaller number of model or principal coordinates. Subspace free decay time responses are computed using properly scaled complex modal vectors. Companion matrix for the general case of nonproportional damping is then derived in the selected vector subspace. Subspace normal modes are obtained through eigenvalue solution of the (M sub N) sup -1 (K sub N) matrix and transformed back to the physical coordinates to get a set of normal modes. A numerical example is presented to demonstrate the outlined theory