Search results for: n-strongly Gorenstein projective

Authors: Jianmin Xing Wei Shao

Abstract:

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the character module of an n -strongly Gorenstein flat left R -module is an n-strongly Gorenstein injective right R -module . At last, let R be a commutative ring and S a multiplicatively closed set of R , we establish the relation between n -strongly Gorenstein projective (injective , flat ) R -modules and n-strongly Gorenstein projective (injective , flat ) S−1R-modules. All conclusions in this paper is helpful for the research of Gorenstein dimensions in future.

Keywords: Commutative ring, n-strongly Gorenstein projective, n-Strongly Gorenstein injective, n-strongly Gorenstein flat, S-ring.

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Authors: Jianmin Xing Wei Shao

Abstract:

We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained.

Keywords: Faithfully balanced self-orthogonal module, ω-Gorenstein module, strongly ω-Gorenstein module, finite generated.

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Authors: Jianmin Xing, Rufeng Xing

Abstract:

In this paper we study some properties of GC-projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC-projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

Keywords: Semidualizing module, C-projective(injective, flat), GC-projective (injective, flat), Commutative ring; Localizations .

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Authors: Basri Çelik

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In this paper, the notion of Hyperbolic Klingenberg plane is introduced via a set of axioms like as Affine Klingenberg planes and Projective Klingenberg planes. Models of such planes are constructed by deleting a certain number m of equivalence classes of lines from a Projective Klingenberg plane. In the finite case, an upper bound for m is established and some combinatoric properties are investigated.

Keywords: Hyperbolic planes, Klingenberg planes, Projective planes.

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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Authors: S. M. Lee, J. H. Park, H. Y. Jung

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This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.

Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.

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Authors: Alexandr A. Penin

Abstract:

Application of projective geometry to the theory of two-ports and cascade circuits with a load change is considered. The equations linking the input and output of a two-port are interpreted as projective transformations which have the invariant as a cross-ratio of four points. This invariant has place for all regime parameters in all parts of a cascade circuit. This approach allows justifying the definition of a regime and its change, to calculate a circuit without explicitly finding the aparameters, to transmit accurately an analogue signal through the unstable two-port.

Keywords: Circuit regime, geometric circuit theory, projective geometry, two-port.

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Authors: Tae H. Lee, J.H. Park, S.M. Lee, H.Y. Jung

Abstract:

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results.

Keywords: Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method

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Authors: Youssef Chahir, Messaoud Mostefai, Salah Khodja

Abstract:

This paper presents the development of a 2D visual marker, derived from a recent patented work in the field of numbering systems. The proposed fiducial uses a group of projective invariant straight-line patterns, easily detectable and remotely recognizable. Based on an efficient data coding scheme, the developed marker enables producing a large panel of unique real time identifiers with highly distinguishable patterns. The proposed marker Incorporates simultaneously decimal and binary information, making it readable by both humans and machines. This important feature opens up new opportunities for the development of efficient visual human-machine communication and monitoring protocols. Extensive experiment tests validate the robustness of the marker against acquisition and geometric distortions.

Keywords: visual marker, projective invariants, distance map, level set

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: Atilla Akpinar, Basri Celik, Suleyman Ciftci

Abstract:

In this paper, we carry over some of the results which are valid on a certain class of Moufang-Klingenberg planes M(A) coordinatized by an local alternative ring A := A(ε) = A+Aε of dual numbers to finite projective Klingenberg plane M(A) obtained by taking local ring Zq (where prime power q = pk) instead of A. So, we show that the collineation group of M(A) acts transitively on 4-gons, and that any 6-figure corresponds to only one inversible m ∈ A.

Keywords: finite Klingenberg plane, projective collineation, 4-transitivity, 6-figures.

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Authors: A. A. Penin

Abstract:

Requirements that should be met when determining the regimes of circuits with variable elements are formulated. The interpretation of the variations in the regimes, based on projective geometry, enables adequate expressions for determining and comparing the regimes to be derived. It is proposed to use as the parameters of a generalized equivalent generator of an active two-pole with changeable resistor such load current and voltage which provide the current through this resistor equal to zero.

Keywords: Equivalent generator, geometric circuits theory, circuits regimes, load characteristics, variable elements.

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Authors: Atilla Akpinar, Basri Çelik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We introduce two new collineations of M(A).

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation.

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Authors: Atilla Akpinar, Basri Celik, Suleyman Ciftci

Abstract:

In this paper, we deal with finite projective Klingenberg plane M (A) coordinatized by local ring A := Zq+Zq E (where prime power q = p', e0 Z q and 62 = 0). So, we get some combinatorical results on 6-figures. For example, we show that there exist p — 1 6-figure classes in M(A).

Keywords: finite Klingenberg plane, 6-figure, ratio of 6-figure, cross-ratio.

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Authors: Shiji Hu, Lei Li, Wanting Zhou, Daohong Yang

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The data encryption is the foundation of today’s communication. On this basis, to improve the speed of data encryption and decryption is always an important goal for high-speed applications. This paper proposed an elliptic curve crypto processor architecture based on SM2 prime field. Regarding hardware implementation, we optimized the algorithms in different stages of the structure. For modulo operation on finite field, we proposed an optimized improvement of the Karatsuba-Ofman multiplication algorithm and shortened the critical path through the pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between the affine coordinate system and the Jacobi projective coordinate system. In the parallel scheduling point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU (dual-core ARM Cortex-A9).

Keywords: Elliptic curve cryptosystems, SM2, modular multiplication, point multiplication.

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Authors: Atilla Akpinar

Abstract:

In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.

Keywords: Finite Klingenberg plane, finite hyperbolic Klingenberg plane.

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Authors: Suleyman Ciftci, Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that some collineations of M(A) preserve cross-ratio.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio.

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Authors: K.M.Goh, M.M.Mokji, S.A.R. Abu-Bakar

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Speeded-Up Robust Feature (SURF) is commonly used for feature matching in stereovision because of their robustness towards scale changes and rotational changes. However, SURF feature cannot cope with large viewpoint changes or skew distortion. This paper introduces a method which can help to improve the wide baseline-s matching performance in term of accuracy by rectifying the image using two vanishing points. Simplified orientation correction was used to remove the false matching..

Keywords: Affine, orientation, projective, SURF.

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Authors: Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that a collineation of M(A) preserve cross-ratio. Also, we obtain some results about harmonic points.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonic points.

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Authors: Z. Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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Authors: Thang Manh Hoang

Abstract:

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

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Authors: Puzanova Zhanna Vasilyevna, Larina Tatiana Igorevna, Tertyshnikova Anastasia Gennadyevna

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In this day and age, extremism in various forms of its manifestation is a real threat to the world community, the national security of a state and its territorial integrity, as well as to the constitutional rights and freedoms of citizens. Extremism, as it is known, in general terms described as a commitment to extreme views and actions, radically denying the existing social norms and rules. Supporters of extremism in the ideological and political struggles often adopt methods and means of psychological warfare, appeal not to reason and logical arguments, but to emotions and instincts of the people, to prejudices, biases, and a variety of mythological designs. They are dissatisfied with the established order and aim at increasing this dissatisfaction among the masses. Youth extremism holds a specific place among the existing forms and types of extremism. In this context in 2015, we conducted a survey among Moscow college and high school students. The aim of this study was to determine how great or small is the difference in understanding and attitudes towards extremism manifestations, inclination and readiness to take part in extremist activities and what causes this predisposition, if it exists. We performed multivariate analysis and found the Russian college and high school students' opinion about the extremism and terrorism situation in our country and also their cognition on these topics. Among other things, we showed, that the level of aggressiveness of young people were not above the average for the whole population. The survey was conducted using the questionnaire method. The sample included college and high school students in Moscow (642 and 382, respectively) by method of random selection. The questionnaire was developed by specialists of RUDN University Sociological Laboratory and included both original questions (projective questions, the technique of incomplete sentences), and the standard test Dayhoff S. to determine the level of internal aggressiveness. It is also used as an experiment, the technique of study option using of FACS and SPAFF to determine the psychotypes and determination of non-verbal manifestations of emotions. The study confirmed the hypothesis that in respondents’ opinion, the level of aggression is higher today than a few years ago. Differences were found in the understanding of and respect for such social phenomena as extremism, terrorism, and their danger and appeal for the two age groups of young people. Theory of psychotypes, SPAFF (specific affect cording system) and FACS (facial action cording system) are considered as additional techniques for the diagnosis of a tendency to extreme views. Thus, it is established that diagnostics of acceptance of extreme views among young people is possible thanks to simultaneous use of knowledge from the different fields of socio-humanistic sciences. The results of the research can be used in a comparative context with other countries and as a starting point for further research in the field, taking into account its extreme relevance.

Keywords: Extremism, youth extremism, diagnostics of extremist manifestations, forecast of behavior, Sociological polls, theory of psychotypes, FACS, SPAFF.

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