Quantitative analysis of arterial spin labeling FMRI data using a general linear model

Arterial spin labeling techniques can yield quantitative measures of perfusion by fitting a kinetic model to difference images (tagged-control). Because of the noisy nature of the difference images investigators typically average a large number of tagged versus control difference measurements over long periods of time. This averaging requires that the perfusion signal be at a steady state and not at the transitions between active and baseline states in order to quantitatively estimate activation induced perfusion. This can be an impediment for functional magnetic resonance imaging task experiments. In this work, we introduce a general linear model (GLM) that specifies Blood Oxygenation Level Dependent (BOLD) effects and arterial spin labeling modulation effects and translate them into meaningful, quantitative measures of perfusion by using standard tracer kinetic models. We show that there is a strong association between the perfusion values using our GLM method and the traditional subtraction method, but that our GLM method is more robust to noise.     

Discussion of the metric in characterizing the single-event effect induced by heavy ions

The single-event effect(SEE) is the most serious problem in space environment.The modern semiconductor technology is concerned with the feasibility of the linear energy transfer(LET) as metric in characterizing SEE induced by heavy ions.In this paper,we calibrate the detailed static random access memory(SRAM) cell structure model of an advanced field programmable gate array(FPGA) device using the computer-aided design tool,and calculate the heavy ion energy loss in multi-layer metal utilizing Geant4.Based on the heavy ion accelerator experiment and numerical simulation,it is proved that the metric of LET at the device surface,ignoring the top metal material in the advanced semiconductor device,would underestimate the SEE.In the SEE evaluation in space radiation environment the top-layers on the semiconductor device must be taken into consideration.     

Discussion of the metric in characterizing single-event effect induced by heavy ions

Single-event effect (SEE) is the most serious problem in space environment. The modern semiconductor technology worries about the feasibility of the linear energy transfer (LET) as metric in characterizing SEE induced by heavy ions. In the paper, we calibrate the detailed static random access memory (SRAM) cell structure model of advanced field programmable gate array (FPGA) device using the computer-aided design tool, and calculate the heavy ion energy loss in multi-layer metal utilizing Geant4. Based on the heavy ion accelerator experiment and numerical simulation, it is proved that the metric of LET at the device surface, with ignoring the top metal material in advanced semiconductor device, would underestimate the SEE. In the SEE evaluation in space radiation environment the top-layers on the semiconductor device must be taken into consideration.     

Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

The Kerr metric in cosmological background

A metric satisfying Einstein’s equations is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a homogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.     

Kerr-Newman metric in deSitter background

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.     

Solutions of Euler-Lagrange equations for self-interacting field of linear frames on product manifold of group space

We investigate a model of self-interacting field of linear frames on the product manifold M × G, where G is a semisimple Lie group acting freely and transitively on a manifold M. We find two families of solutions of the Euler-Lagrange equations for the field of frames.     

五维时空中度规的计算

在四维R+R2引力理论中给出了Wheeler-Dewitt(W-D)方程,通过分离变量法得到了W-D方程的解.利用Kaluza-Klein理论将Robertson-Walker度规推广到五维时空,结合时空中的场方程得到宇宙项与能量之间的关系.     

The foundations of the poincaré group and the validity of general relativity

After discussions about accepted ideas concerning the nonlocalisability of the photon, the interpretation of the Minkowski space-time, the wave-corpuscle duality ideas of Niels Bohr and the concept of elementary particle by Eugene Wigner, the validity of the Poincaré group is brought into question and some other ideas are developed. Lukierski, Nowicki and Ruegg showed that the successes of the Poincaré group are preserved if we deform the group by introducing a constant κ. Such deformation replaces the Poincaré Hopf algebra by another one. We call such a deformation a mathematical deformation. The main inconvenience of this mathematical deformation is that the coproduct is not commutative. The consequence is that a two-particle state is defined in an ambiguous way because we must say which is the first particle and which is the second one. The only mathematical deformation of the Poincaré group which preserves the commutativity of the coproduct is the trivial one, that is the Poincaré Hopf algebra itself. That is why we reject the mathematical deformation of Lukierski, Nowicki and Ruegg. That is also why we propose what we call a physical deformation of the Poincaré group, which means that we reinterpret the Poincaré Hopf algebra, with the same constant κ. Our proposal has four advantages:

1.

1. The constant x has the dimensions of a mass. When this constant becomes infinite, we are left with the Poincaré group with its main successes.

2.

2. The two-particle states are unambiguously defined.

3.

3. The constant κ may be chosen in such a way that the search for a missing mass in the universe is useless.

4.

4. It consists in the disappearing of unphysical irreducible representations of the Poincaré group.

With the constant κ, we arrive at a reformulation of special relativity where the energy is no longer additive. This would imply a change in general relativity where the density of matter must be different from the density of energy. Unfortunately, we are not able to propose a substitute for the general relativity theory. Obviously, when the constant κ goes to infinity, the new general relativity would become the standard general relativity.     

Covariant fields: Poincaré group representations and metric structure in the space of quantum states

The representations of the Poincaré group realized over the space of covariant fields transforming according to any irreducible representationD ^(m,n) of the Lorentz group are constructed explicitly with reference to a helicity basis. The representation is indecomposable in the massless case. The form of this representation together with the invariance of two-point Wightman functions of the field (which follows from a weak set of axioms) determines the metric structure in the space of quantum states of the field. This structure is explicitly determined for generalD ^(m,n). Certain particular cases (especially the symmetric traceless tensor field) are discussed in detail. Finally we consider the representation pertaining to massive fields, and examine the passage to the limit of vanishing mass. We present a limiting procedure which leads from the unitary representation of the massive field to the indecomposable non-unitary representation of the massless field.     

On invariant and covariant Schwartz distributions in the case of a compact linear group

A proof is given for the representations of invariant and covariant (Schwartz) distributions onR ⁿ , which are often used in theoretical physics. We express invariant distributions as distributions of standard polynomial invariants and decompose covariant distributions in standard polynomial covariants. Our consideration is restricted to compact groups acting linearly onR ⁿ . The representation for invariant distributions is obtained provided the standard invariants form an algebraically independent generating set in the ring of invariant polynomials. As for the standard covariants we assume that in the class of covariant polynomials they provide a unique decomposition into a sum of the standard covariants multiplied with invariant polynomials.     

运用线性量子变换理论和定态微扰论求解线型多原子分子振动的一般方法

采用键长伸缩和垂直键轴位移为内坐标,多维耦合谐振子、势函数中超过二次幂的项分别为零级近似和微扰的线型多原子分子振动模型,运用广义线性量子变换理论和定态微扰论对线型多原子分子振动进行了普遍求解,将线型多原子分子简谐振动能量本征值和态的求解转化成正定和半正定矩阵的对角化问题,微扰矩阵元、能量和波函数各级修正的计算转换到多维无耦合谐振子的本征表象中进行.并以CO2分子为例进行了具体求解.     

Accelerated Levi-Civita-Bertotti-Robinson metric in D dimensions

A conformally flat accelerated charge metric is found in an arbitrary dimension D. It is a solution of the Einstein-Maxwell-null fluid equations with a cosmological constant in D ≥ 4 dimensions. When the acceleration is zero, our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.     

The series solution to the metric of stationary vacuum with axisymmetry

The multipole moment method not only conduces to the understanding of the deformation of the space--time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.     

Saddle-node bifurcation of invariant cones in 3D piecewise linear systems

In this work, the existence of a saddle-node bifurcation of invariant cones in three-dimensional continuous homogeneous piecewise linear systems is considered. First, we prove that invariant cones for this class of systems correspond one-to-one to periodic orbits of a continuous piecewise cubic system defined on the unit sphere. Second, let us give the conditions for which the sphere is foliated by a continuum of periodic orbits. The principal idea is looking for the periodic orbits of the continuum that persist when this situation is perturbed. To do this, we establish the relationship between the invariant cones of the three-dimensional system and the periodic orbits of two planar hybrid piecewise linear systems. Next, we define two functions whose zeros provide the invariant cones that persist under the perturbation. These functions will be called Melnikov functions and their properties allow us to state some results about the existence of invariant cones and other results about the existence of saddle-node bifurcations of invariant cones, which is the principal goal of this paper.     

On quantum symmetries of compact metric spaces

An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. In this study, we show that an isometric action in this sense has the following additional property: the corresponding action on the algebra of continuous functions on $X$ by the convolution semigroup of probability measures on the quantum group contracts Lipschitz constants. In other words, it is isometric in another sense due to Li, Quaegebeur, and Sabbe, which partially answers a question posed by Goswami. We also introduce other possible notions of isometric quantum actions in terms of the Wasserstein $p$-distances between probability measures on $X$ for $p\ge 1$, which are used extensively in optimal transportation. Indeed, all of these definitions of quantum isometry belong to a hierarchy of implications, where the two described above lie at the extreme ends of the hierarchy. We conjecture that they are all equivalent.     

Exact Scalar Field Inflationary Solution in Rainbow Universe

Using the Friedmann equation in rainbow Universe, we obtain an exact scalar field Inflationary Solution, which is a modification of the exact scalar field with negative potential −V ₀+m ² φ ²/2. Because the rainbow metric is Finsler metric, the result in this paper implies that the research of Finsler geometry in Cosmology should lead to several new physics theories.