scholarly journals Measure Theoretic Entropy of Discrete Geodesic Flow on Nagao Lattice Quotient

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 52
Author(s):  
Sanghoon Kwon
Keyword(s):  
Geodesic Flow ◽  
Probability Measures ◽  
Diagonal Action ◽  
The Right

The discrete geodesic flow on Nagao lattice quotient of the space of bi-infinite geodesics in regular trees can be viewed as the right diagonal action on the double quotient of PGL2Fq((t−1)) by PGL2Fq[t] and PGL2(Fq[[t−1]]). We investigate the measure-theoretic entropy of the discrete geodesic flow with respect to invariant probability measures.

scholarly journals Equidistribution results for geodesic flows

2013 ◽  
Vol 34 (3) ◽  
pp. 742-764
Author(s):  
ABDELHAMID AMROUN
Keyword(s):  
Geodesic Flow ◽  
Large Deviation ◽  
Riemannian Metric ◽  
Upper Bounds ◽  
Equilibrium States ◽  
Topological Pressure ◽  
Probability Measures ◽  
Geodesic Flows ◽  
Lower And Upper Bounds ◽  
Unit Tangent Bundle

AbstractUsing the works of Mañé [On the topological entropy of the geodesic flows.J. Differential Geom.45(1989), 74–93] and Paternain [Topological pressure for geodesic flows.Ann. Sci. Éc. Norm. Supér.(4)33(2000), 121–138] we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a$\mathcal {C}^{\infty }$Riemannian metric. We prove large-deviation lower and upper bounds and a contraction principle for the geodesic flow in the space of probability measures of the unit tangent bundle. We deduce a way of approximating equilibrium states for continuous potentials.

scholarly journals psi-Hilfer Fractional Approximations of Csiszar's f-Divergence

2021 ◽  
Author(s):  
George Anastassiou
Keyword(s):  
Fractional Derivatives ◽  
Random Variables ◽  
Probability Measures ◽  
General Measure ◽  
Essential Aspect ◽  
Probabilistic Inequalities ◽  
The Right ◽  
Measure Of Dependence ◽  
Derivatives Of ◽  
Best Estimates

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

ON SIMPLEX SHAPE SPACES

2001 ◽  
Vol 64 (2) ◽  
pp. 501-512 ◽  
Author(s):  
HUILING LE ◽  
DENNIS BARDEN
Keyword(s):  
Shape Analysis ◽  
Symmetric Spaces ◽  
Riemannian Metric ◽  
Probability Measures ◽  
Geometric Features ◽  
Compact Type ◽  
Typical Application ◽  
Shape Spaces ◽  
Riemannian Symmetric Spaces ◽  
The Right

The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to that for Kendall's shape spaces.

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

New Dimensions in Freeze-Etching

1969 ◽  
Vol 27 ◽  
pp. 202-203 ◽  
Author(s):  
Russell L. Steere ◽  
Michael Moseley
Keyword(s):  
Fracture Surfaces ◽  
Aluminum Specimen ◽  
Specimen Holder ◽  
Freeze Etching ◽  
The Right

A redesigned specimen holder and cap have made possible the freeze-etching of both fracture surfaces of a frozen fractured specimen. In principal, the procedure involves freezing a specimen between two specimen holders (as shown in A, Fig. 1, and the left side of Fig. 2). The aluminum specimen holders and brass cap are constructed so that the upper specimen holder can be forced loose, turned over, and pressed down firmly against the specimen stage to a position represented by B, Fig. 1, and the right side of Fig. 2.

Adrenocorticotropin Production by a Mammary Carcinoma

1977 ◽  
Vol 35 ◽  
pp. 462-463
Author(s):  
K.S. McCarty ◽  
N.R. Wallace ◽  
W. Litaker ◽  
S. Wells ◽  
G. Eisenbarth
Keyword(s):  
Adrenocorticotropic Hormone ◽  
Small Cell ◽  
Hormone Production ◽  
Carcinoma Of The Breast ◽  
Ectopic Acth ◽  
Ultrastructural Studies ◽  
Subcutaneous Metastases ◽  
Ectopic Acth Production ◽  
The Right ◽  
Pituitary Carcinomas

The production of adrenocorticotropic hormone by non-pituitary carcinomas has been documented in several tumors, most frequently small cell carcinoma of the lung, islet cell carcinomas of the pancreas, thymomas and carcinoids. Electron microscopy of these tumors reveals typical membrane-limited "neurosecretory" granules. Confirmation of the granules as adrenocorticotropin (ACTH) requires the use of OsO4 as a primary fixative to give the characteristic cored granule appearance in conjunction with immunohistochemical demonstration of the hormone peptide. Because of the rarity of ectopic ACTH production by mammary carcinomas and the absence of appropriate ultrastructural studies in the two examples of such ectopic hormone production in the literature of which we are aware (1,2), we present biochemical and ultrastructural data from a carcinoma of the breast with apparent ACTH production.The patient had her primary tumor in the right breast in 1969. The tumor recurred as visceral and subcutaneous metastases in 1976 and again in 1977.

Z-line degradation and phagocytosis of sarcomeric fragments in myonecrosis

1983 ◽  
Vol 41 ◽  
pp. 790-791
Author(s):  
Melinda L. Estes ◽  
Samuel M. Chou
Keyword(s):  
Vastus Lateralis ◽  
Inflammatory Myopathy ◽  
Muscle Disease ◽  
White Female ◽  
Inflammatory Cell Infiltrate ◽  
Limb Weakness ◽  
Muscle Diseases ◽  
History Of ◽  
The Right ◽  
Mononuclear Inflammatory Cell

Many muscle diseases show common pathological features although their etiology is different. In primary muscle diseases a characteristic finding is myofiber necrosis. The mechanism of myonecrosis is unknown. Polymyositis is a primary muscle disease characterized by acute and subacute degeneration as well as regeneration of muscle fibers coupled with an inflammatory infiltrate. We present a case of polymyositis with unusual ultrastructural features indicative of the basic pathogenetic process involved in myonecrosis.The patient is a 63-year-old white female with a one history of proximal limb weakness, weight loss and fatigue. Examination revealed mild proximal weakness and diminished deep tendon reflexes. Her creatine kinase was 1800 mU/ml (normal < 140 mU/ml) and electromyography was consistent with an inflammatory myopathy which was verified by light microscopy on biopsy muscle. Ultrastructural study of necrotizing myofiber, from the right vastus lateralis, showed: (1) degradation of the Z-lines with preservation of the adjacent Abands including M-lines and H-bands, (Fig. 1), (2) fracture of the sarcomeres at the I-bands with disappearance of the Z-lines, (Fig. 2), (3) fragmented sarcomeres without I-bands, engulfed by invading phagocytes, (Fig. 3, a & b ), and (4) mononuclear inflammatory cell infiltrate in the endomysium.

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