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.

Irreducibility in M_n(C)

In this paper, we investigate the irreducibility of the n×n complex matrix and obtain the following result: For each A in Mn(C), let λ1, λ2,…,λm be all eigenvalues of A, where m≤n and λi≠λj if i≠j. Then A is irreducible if and only if for each P in A' (A) and P* = P = P2,we have σ(P\ker(A - λ1)) =σ(P\ker(A - λ2)) = …= σ(P\ker(A - λm)) = singleton.

The Irreducibility and Isomorphism of Piecewise Algebraic Sets

In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.

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

Two Classes of Operators with Irreducibility and the Small and Compact Perturbations of Them

This paper gives the concepts of finite dimensional irreducible operators（（FDI） operators）and infinite dimensional irreducible operators（（IDI） operators）. Discusses the relationships of（FDI）operators,（IDI） operators and strongly irreducible operators（（SI） operators） and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an（FDI） operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in（Σ FDI）（X） with respect to the strong-operator topology and every compact operator K can be approximated by operators in（Σ FDI）（X） with respect to the norm topology on a Banach space X with a Schauder basis, where（ΣFDI）（X） ：= {T∈B（X） ： T=Σki=1Ti, Ti ∈（FDI）, k ∈ N}.

The Emergence and Irreducibility of Scientific Knowledge： A Multi-Synergic-Holism

The world possesses a hierarchical structure and evolves through emergence. Its levels are the result of emergence, and possess unique properties and functions which their components and emergent bases do not. Each of these levels also possesses basic laws or rules which cannot be logically deduced from other levels, and evince downward causation. Therefore, there are non-linear causal networks among the levels of complex systems in which causal reductionism does not hold. The hierarchical structure is formed in accordance with the increasing organized complexity of the objects, so that different levels give birth to different disciplines, and different disciplines have their own theoretical autonomy and independence. Therefore, theories across different levels are essentially irreducible, and any apparent case of reduction may only be so in the sense of a partial reduction. Emergence-evolution-hierarchy ontology and multi-synergic holism is compatible with reductionism even as it transcends it.

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

Irreducibility Properties of Keller Maps

Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map over a field of characteristic zero is a Keller map, if and only if the corresponding endomorphism maps irreducible polynomials to square-free polynomials. We show that the latter endomorphism maps other square-free polynomials to square-free polynomials as well. In connection with the above classification of invertible polynomial maps and the Jacobian Conjecture, we study irreducibility properties of several types of Keller maps, to each of which the Jacobian Conjecture can be reduced. Herewith, we generalize the result of Bakalarski that the components of cubic homogeneous Keller maps with a symmetric Jacobian matrix （over C and hence any field of characteristic zero） are irreducible. Furthermore, we show that the Jacobian Conjecture can even be reduced to any of these types with the extra condition that each affinely linear combination of the components of the polynomial map is irreducible. This is somewhat similar to reducing the planar Jacobian Conjecture to the so-called （planar） weak Jacobian Conjecture by Kaliman.

A C~*-ALGEBRA APPROACHTO THE IRREDUCIBILITY OFCOWEN-DOUGLAS OPERATORS

The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn+1 Ker Tn) is M.(C).

The Necessary and Sufficient Condition for Strong Irreducibility of Cowen-Douglas Operators

In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ （D）, where D is the open unit disk, and H^∞（D） denotes the collection of bounded holomorphic functions on D.

THE(U+K)-ORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation. This partially answers a question of Domigo A. Herrero.

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.

The Effect of Temperature on Irreducible Water Saturation of Water-wet Cores

The conventional measurement of a relative permeability curve (RPC) is usually conducted at room temperature, which is much lower than the reservoir temperature. Previous research work on high temperature relative permeability mainly take oil-wetted cores as objective. In this paper, laboratory test and measurement are conducted using water-wet cores from the Lunnan Oilfield. Since irreducible water saturation (Swi) is a critical factor that affects and controls the relative permeability curve, special tests are conducted to measure Swi at different temperatures for water-wet cores in the course of the experiment of relative permeability. The experimental results indicate that for the water-wet cores Swi decreased with the increasing temperature from ambient to 105℃,and the relative permeability curve shifted in a low water saturation direction, i.e. moved toward the left, while it moved toward the right for oil wetness reservoirs. Seen from both macroscopic and microcosmic view, the reasons and mechanisms of relative permeability change with temperature are discussed, and factors including core wetness, viscosity force, capillary forces, contact angle, interfacial tension change are considered.

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.

The Asymptotic Stability for a Class of Nonlinear Large Sceale System

This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.