The symmetric space,strong isotropy irreducibility and equigeodesic properties

A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

Improving Video Watermarking through Galois Field GF(2^(4)) Multiplication Tables with Diverse Irreducible Polynomials and Adaptive Techniques

Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4)),and their interaction with distinct irreducible polynomials.The primary aim is to enhance watermarking techniques for achieving imperceptibility,robustness,and efficient execution time.The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process.Scene selection is used strategically to embed watermarks in the most vital frames of the video,while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria,maintaining the video's visual quality.Concurrently,careful consideration is given to execution time,crucial in real-world scenarios,to balance efficiency and efficacy.The Peak Signal-to-Noise Ratio(PSNR)serves as a pivotal metric to gauge the watermark's imperceptibility and video quality.The study explores various irreducible polynomials,navigating the trade-offs between computational efficiency and watermark imperceptibility.In parallel,the study pays careful attention to the execution time,a paramount consideration in real-world scenarios,to strike a balance between efficiency and efficacy.This comprehensive analysis provides valuable insights into the interplay of GF multiplication tables,diverse irreducible polynomials,scene selection,adaptive thresholding,imperceptibility,and execution time.The evaluation of the proposed algorithm's robustness was conducted using PSNR and NC metrics,and it was subjected to assessment under the impact of five distinct attack scenarios.These findings contribute to the development of watermarking strategies that balance imperceptibility,robustness,and processing efficiency,enhancing the field's practicality and effectiveness.

CRITERIONS AND ALGORITHMS FOR IRREDUCIBILITY AND APERIODICITY OF NONNEGATIVE MATRICES

The irreducibility and aperiodicity (primitivity)are two basic notions in the theory of nonnegative matrices. As we know, for a nonnegative matrix, there exist no feasible algorithms for judging them, especially for aperiodicity. Usually, for a k×k nonnegative matrix, one can form an associated directed graph which has k vertices and whose directed

WEAK IRREDUCIBILITY OF MATRIX AND SPECTRAL INCLUSION REGIONS

Let Г(A) be a directed graph of the matrix A of order n. We say that A is weakly irreducible, if every vertex of Г(A) belongs to some circuit of Г(A). A matrix is weakly irreducible iff there exists a permutation matrix P of order n such

A new NMR-data-based method for predicting petrophysical properties of tight sandstone reservoirs

Evaluating the permeability and irreducible water saturation of tight sandstone reservoirs is challenging.This study uses distribution functions to fit measured NMR T_(2)distributions of tight sandstone reservoirs and extract parameters for characterizing pore size distribution.These parameters are then used to establish prediction models for permeability and irreducible water saturation of reservoirs.Results of comparing the fit of the T_(2)distributions by the Gauss and Weibull distribution functions show that the fitting accuracy with the Weibull distribution function is higher.The physical meaning of the statistical parameters of the Weibull distribution function is defined to establish nonlinear prediction models of permeability and irreducible water saturation using the radial basis function(RBF)method.Correlation coefficients between the predicted values by the established models and the measured values of the tight sandstone core samples are 0.944 for permeability and 0.851 for irreducible water saturation,which highlight the effectiveness of the prediction models.

Modeling the Dynamics of the Random Demand Inventory Management System

At any given time, a product stock manager is expected to carry out activities to check his or her holdings in general and to monitor the condition of the stock in particular. He should monitor the level or quantity available of a given product, of any item. On the basis of the observation made in relation to the movements of previous periods, he may decide to order or not a certain quantity of products. This paper discusses the applicability of discrete-time Markov chains in making relevant decisions for the management of a stock of COTRA-Honey products. A Markov chain model based on the transition matrix and equilibrium probabilities was developed to help managers predict the likely state of the stock in order to anticipate procurement decisions in the short, medium or long term. The objective of any manager is to ensure efficient management by limiting overstocking, minimising the risk of stock-outs as much as possible and maximising profits. The determined Markov chain model allows the manager to predict whether or not to order for the period following the current period, and if so, how much.

Study on Geological Genesis and Sedimentary Model of Complex Low Resistivity Reservoir in Offshore Oilfield — A Case of NgIII Formation of X Oilfield in Bohai Sea

In order to study the micro genetic mechanism and main geological controlling factors of low resistivity reservoir in NgIII formation of X oilfield in Bohai sea in China, the clay mineral composition, irreducible water saturation, salinity and conductive minerals of low resistivity reservoir were studied by using the data of core, cast thin section and analysis, and compared with normal resistivity reservoir. At the same time, the control effect of sedimentary environment on low resistivity reservoir was discussed. The results show that the additional conductivity of high bound water content and high montmorillonite content in the reservoir together leads to the significant reduction of reservoir resistivity, which is the main microscopic cause of the formation of low resistance, and is mainly controlled by the sedimentary background such as paleoclimate and sedimentary cycle. During the deposition period of NgIII formation, the paleoclimate was dry and cold, and it was at the end of the water advance of the medium-term sedimentary cycle. The hydrodynamic force of the river channel was weak, the carrying capacity of the riverbed was weak, and the river channel swayed frequently, resulting in fine lithologic particle size, high shale content and complex pore structure of the reservoir, resulting in significant reduction of reservoir resistance. The research conclusion would have strong guiding significance for the development of low resistivity reservoirs in this area.

Pore structure characterization based on NMR experiment: A case from the Shanxi Formation tight sandstones in the Daning-Jixian area, eastern Ordos Basin

The study of pore structure requires consideration of important factors including pore throat size,pore radius composition,and pore-throat configuration.As the nuclear magnetic resonance(NMR)experimental results contain rich information about pore structures and fluid occurrence states,this study investigated the pore structures of the tight sandstone reservoirs of the Shanxi Formation in the Daning-Jixian area,eastern Ordos Basin.Firstly,by making the inverse cumulative curve of the NMR T2 spectrum coincide with the capillary pressure curves which were obtained by the mercury injection capillary pressure(MICP)technique,this study derived a conversion coefficient that can be used to convert the NMR T2 spectrum into the pore throat radius distribution curves based on the NMR experimental results.Subsequently,we determined the pore radius intervals corresponding to irreducible water distribution using the NMR-derived pore radius distribution curves.Finally,the NMR T2 distribution curves based on the fractal theory were analyzed and the relationships between fractal dimensions and parameters,including permeability,porosity,reservoir quality index(RQI),flow zone indicator(FZI),irreducible water saturation,RT35,and RT50,were also discussed.The NMR-derived pore throat radius distribution curves of the study area are mainly unimodal,with some curves showing slightly bimodal distributions.The irreducible water mainly occurs in small pores with a pore radius less than 100 nm.As the permeability decreases,the contribution rate of small pores to the irreducible water gradually increases.The NMR-based fractal dimensions of pores show a two-segment distribution.Small pores have small fractal dimensions and are evenly distributed,while large pores have large fractal dimensions and complex pore structures.The fractal dimension of large pores(Dmax)is poorly correlated with porosity but strongly correlated with FZI,RQI,RT35,and RT50.These results indicate that large pores are the main pore zones that determine the seepage capacity of the reservoirs.Additionally,there is a certain correlation between Dmax and the irreducible water saturation.

Isotropic polynomial invariants of Hall tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

Asymptotic Stability of the Dynamic Solution of an N-Unit Series System with Finite Number of Vacations

We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

The Geometrical Theory of the Structure of Nuclei, Atoms, and Molecules

Quantum geometrodynamics (QGD) has established the following fundamental facts: First, every elementary particle is the physical realization of a certain irreducible 4-quantum operator of spin (rank) 0, 1/2 or 1. A photon (boson) is the physical realization of an irreducible 4-quantum operator of spin zero. A fermion is the physical realization of an irreducible 4-quantum operator of spin 1/2. A graviton (boson) is the physical realization of an irreducible 3-quantum operator of spin zero, and the Ws and mesons (bosons) are the physical realizations of irreducible 3-quantum operator of rank one. Second, the particles of every composite fermion system (nuclei, atoms, and molecules) reside in a certain 4-quantum space which is partitioned into an infinite set of subspaces of dimension 4n (n = 1, 2, 3, L,?∞;n is the index of the subspace and n is called principal quantum number by physicists, and period by chemists) each of which is reducible to a set of 2-level cells [1]. With these two fundamental facts, the complexities associated with atomic, nuclear, and molecular many-body problems have evaporated. As an application of the reducibility scenario we discuss in this paper the explicit construction of the periodic table of the chemical elements. In particular we show that each chemical element is characterized by a state ket |En;l, m1;s, ms〉where l is orbital angular momentum, s = 1/2, En = E1 + khv (k = 1, 2, 3, L, ∞, E1 is the Schr?dinger first energy level, and v is the Lamb-Retherford frequency).

Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

Asymptotic Stability of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations

We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

Inhomogeneous Differential Realization, Boson-Fermion Realization of OSP(2,1) Superalgebra and Its Representations

Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.

Posterolateral dislocation of the knee:Recognizing an uncommon entity

Posterolateral dislocations of the knee are rare injuries.Early recognition and emergent open reduction is crucial.A 48-year-old Caucasian male presented with right knee pain and limb swelling 3 d after sustaining a twisting injury in the bathroom.Examination revealed the pathognomonic anteromedial "pucker" sign.Anklebrachial indices were greater than 1.0 and symmetrical.Radiographs showed a posterolateral dislocation of the right knee.He underwent emergency open reduction without an attempt at closed reduction.Attempts at closed reduction of posterolateral dislocations of the knee are usually impossible because of incarceration of medial soft tissue in the intercondylar notch and may only to delay surgical management and increase the risk of skin necrosis.Magnetic resonance imaging is not crucial in the preoperative period and can lead to delays of up to 24 h.Instead,open reduction should be performed once vascular compromise is excluded.

SOME REMARKS ON CCR AND WEYL OPERATORS

Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic and anti-bolomorphic symbols respectively. Further. in the Weyl representation of CCR, three Weyl operators will constitute an irreducible set of the fall CCR-algebra if some number theoretic conditions are satisfied.

Evaluation of clayed silt properties on the behavior of hydrate production in South China Sea

Gas hydrate is one kind of potential energy resources that is buried under deep seafloor or frozen areas.The first trial offshore production from the silty reservoir was conducted in the South China Sea by the China Geological Survey(CGS).During this test,there were many unique characteristics different from the sand reservoir,which was believed to be related to the clayed silt physical properties.In this paper,simulation experiments,facilities analysis,and theoretical calculation were used to confirm the hydrate structure,reservoir thermo-physical property,and bond water movement rule.And the behavior of how they affected production efficiency was analyzed.The results showed that:It was reasonable to use the structure I rather than structure II methane hydrate phase equilibrium data to make the production plan;the dissociation heat absorbed by hydrate was large enough to cause hydrate self-protection or reformation depend on the reservoir thermal transfer and gas supply;clayed silt got better thermal conductivity compared to coarse grain,but poor thermal convection especially with hydrate;clayed silt sediment was easy to bond water,but the irreducible water can be exchanged to free water under high production pressure,and the most obvious pressure range of water increment was 1.9–4.9 MPa.

Electromagnetic Field Released in Collision-Impact Events Generate in the Matrix Interface Fractal Scalable Invariant Geometric Triangular Chiral Hexagonal Structures

In biology, cancer is the most beautiful natural model of a chaotic system, which under uncontrolled proliferations, generates extreme disorder that finally causes intercellular collisions. The authors have described and documented fractal self-assembly of geometric triangular chiral hexagonal crystal-like complex organizations (GTCHC) and interface comet tail effect patterns in cancer processes. According to this novel observation cancer incorporates a real visualization world with a great surprising finding in biology, physics, and geology. This visualization platform literally allows us to see what would otherwise remain completely invisible. From theory to practice this irreducible geometric matrix allowed us to identify in geology, real measurable green infrared-electromagnetic stripe line in interface with hexagonal geomorphic pattern, triangular chiral pyramidal rock structures, geology well defined mirror images, template platform to bio signature characterization of ancestral primitive polar head-tail organization, embryoid and human-like shape pattern embedded as giant fossils in rocks that have never been seen before. Electromagnetic field released in collision-impact events generate in the matrix interphase fractal scalable invariant order of geometric triangular chiral hexagonal structures. The laws of biology and geology can finally be redirected to the laws of physics;specifically magnetic fields create a new kind of classification based on these fractal structural similarities of the relationship. Further interdisciplinary collaboration must be carried out to study these geometric self-assembly geological structures, ancient sediments and rocks that could provide insights into antecedents of life.

Observations on Irreducible Sets and Sober Spaces

This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.