The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year w...The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year with the use of the classification of finite simple groups (CFSG). A series of interesting questions arise naturally. First of all, it is not clear whether it is possible to avoid CFSG or not. On the other hand, what happens for infinite groups? Since the status of knowledge of the non-commuting graph and of the prime graph is satisfactory, is it possible to find relations between these two graphs and the Sylow graph? In the present note we make the point of the situation and formulate the above questions in appropriate way.展开更多
Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commutin...Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.展开更多
Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two...Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two distinct vertices a, b are adjacent if and only if a E S or b E S and ab ≠ ba. We determine the diameter, girth and some dominating sets for FS, K. Some connections between Fs,K and Pr（S, K） are also obtained. Further, Z-isoclinism between two pairs of finite rings is defined, and we show that the generalized non-commuting graphs of two Y_~isoclinic pairs are isomorphic under some conditions.展开更多
Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this p...Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp ×→ × Zp →1 and its derivedsubgroup has order p.展开更多
Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storag...Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storage and access,our proposed work designs a Novel Quantum Key Distribution(QKD)relying upon a non-commutative encryption framework.It makes use of a Novel Quantum Key Distribution approach,which guarantees high level secured data transmission.Along with this,a shared secret is generated using Diffie Hellman(DH)to certify secured key generation at reduced time complexity.Moreover,a non-commutative approach is used,which effectively allows the users to store and access the encrypted data into the cloud server.Also,to prevent data loss or corruption caused by the insiders in the cloud,Optimized Genetic Algorithm(OGA)is utilized,which effectively recovers the data and retrieve it if the missed data without loss.It is then followed with the decryption process as if requested by the user.Thus our proposed framework ensures authentication and paves way for secure data access,with enhanced performance and reduced complexities experienced with the prior works.展开更多
By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topologi...By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.展开更多
We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined t...We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.展开更多
In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time...In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.展开更多
The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a...The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains aterm corresponding to a Wess-Zumino-Witten-like term.展开更多
This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole...This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.展开更多
The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as th...The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.展开更多
For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld inva...For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.展开更多
We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in b...We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces.By considering the Rashba interaction,we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space.We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling.Finally,we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.展开更多
This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings,denoted ΓI（R）.ΓI（R） is a directed graph.The properties and possible structures of the graph is studied.
The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the mod...The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.展开更多
The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, w...The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.展开更多
In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation i...In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.展开更多
The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the ...The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.展开更多
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutativ...The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.展开更多
The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two en...The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two entangled particles neglecting non-commutation. The assumed correlation functions, later confirmed for certain quantum measurements, violate the Bell inequality. The present paper reviews a more general derivation of the Bell inequality showing that it is identically satisfied by finite data sets whether deterministic or random, after assuming merely that they exist. It is thereafter concerned with the consequences of this result for interpretations of the inequality that result in its violation. A primary finding is that correlation functions have differing forms due to quantum commutation, non-commutation, and conditions of measurement, and result in satisfaction of the Bell inequality used consistently with its derivation. A stochastic process having the same correlation function for all variable pairs is shown to be inconsistent with experimentally reported data. The logic of the three and four variable inequalities is shown to be similar. Finally the inequalities in probabilities are shown to follow from those in correlations with quantum mechanical results satisfying either when properly implemented.展开更多
文摘The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved only last year with the use of the classification of finite simple groups (CFSG). A series of interesting questions arise naturally. First of all, it is not clear whether it is possible to avoid CFSG or not. On the other hand, what happens for infinite groups? Since the status of knowledge of the non-commuting graph and of the prime graph is satisfactory, is it possible to find relations between these two graphs and the Sylow graph? In the present note we make the point of the situation and formulate the above questions in appropriate way.
基金The NSF(11301150,11371124)of Chinathe NSF(142300410134)of Henan ProvincePlan for Scientific Innovation Talent(11CXRC19)of Henan University of Technology
文摘Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.
文摘Let S and K be two subrings of a finite ring R. Then the generalized non- commuting graph of subrings S, K of R, denoted by [＇S,K, is a simple graph whose vertex set is （S U K）／（CK（S） U Cs（K））, and where two distinct vertices a, b are adjacent if and only if a E S or b E S and ab ≠ ba. We determine the diameter, girth and some dominating sets for FS, K. Some connections between Fs,K and Pr（S, K） are also obtained. Further, Z-isoclinism between two pairs of finite rings is defined, and we show that the generalized non-commuting graphs of two Y_~isoclinic pairs are isomorphic under some conditions.
基金Project supported by the NSFC （11301150, 11371124）, Natural Science Foundation of Henan Province of China （142300410134）, Program for Innovation Talents of Science and Technology of Henan University of Technology （11CXRC19）.
文摘Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp ×→ × Zp →1 and its derivedsubgroup has order p.
文摘Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storage and access,our proposed work designs a Novel Quantum Key Distribution(QKD)relying upon a non-commutative encryption framework.It makes use of a Novel Quantum Key Distribution approach,which guarantees high level secured data transmission.Along with this,a shared secret is generated using Diffie Hellman(DH)to certify secured key generation at reduced time complexity.Moreover,a non-commutative approach is used,which effectively allows the users to store and access the encrypted data into the cloud server.Also,to prevent data loss or corruption caused by the insiders in the cloud,Optimized Genetic Algorithm(OGA)is utilized,which effectively recovers the data and retrieve it if the missed data without loss.It is then followed with the decryption process as if requested by the user.Thus our proposed framework ensures authentication and paves way for secure data access,with enhanced performance and reduced complexities experienced with the prior works.
基金supported by the National Natural Science Foundation of China (Grant Nos 10575026, 10465004, 10665001 and 10447005)
文摘By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.
文摘We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.
文摘In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.
文摘The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains aterm corresponding to a Wess-Zumino-Witten-like term.
基金DST,New Delhi,India,for its financial support for research facilities under DSTFIST-2019。
文摘This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10575026 and 10875035)the Natural Science Foundation of Zhejiang Province,China (Grant No Y607437)
文摘The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.
文摘For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.
基金the National Elites Foundation(INEF),Iran for financial support under research project No.15/6072。
文摘We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces.By considering the Rashba interaction,we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space.We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling.Finally,we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.
基金Supported by Guangxi Natural Sciences Foundation(0575052,0640070)Supported byInnovation Project of Guangxi Graduate Education(2006106030701M05)Supported Scientific Research Foun-dation of Guangxi Educational Committee
文摘This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings,denoted ΓI（R）.ΓI（R） is a directed graph.The properties and possible structures of the graph is studied.
基金Supported by the China Scholarship Councilthe Hanjiang Scholar Project of Shaanxi University of Technology
文摘The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.
文摘The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.
文摘In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.
文摘The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90303003 and 10575026） and the Natural Science Foundation of Zhejiang Province, China （Grant No M103042）.
文摘The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
文摘The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two entangled particles neglecting non-commutation. The assumed correlation functions, later confirmed for certain quantum measurements, violate the Bell inequality. The present paper reviews a more general derivation of the Bell inequality showing that it is identically satisfied by finite data sets whether deterministic or random, after assuming merely that they exist. It is thereafter concerned with the consequences of this result for interpretations of the inequality that result in its violation. A primary finding is that correlation functions have differing forms due to quantum commutation, non-commutation, and conditions of measurement, and result in satisfaction of the Bell inequality used consistently with its derivation. A stochastic process having the same correlation function for all variable pairs is shown to be inconsistent with experimentally reported data. The logic of the three and four variable inequalities is shown to be similar. Finally the inequalities in probabilities are shown to follow from those in correlations with quantum mechanical results satisfying either when properly implemented.
