فهرست مطالب
Caspian Journal of Mathematical Sciences
Volume:9 Issue: 1, Winter Spring 2020
- تاریخ انتشار: 1399/07/15
- تعداد عناوین: 10
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Pages 1-23This paper develops a basic theory of $H$-groups. We introduce a special quotient of $H$-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups.Keywords: $H$-group, sub-$H$-group, quotient of $H$-group
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Pages 24-38
In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.
Keywords: Weighted composition operators, weighted Bergman spaces, weighted Bloch spaces -
Pages 39-55In this paper, the aim is to find a complex interval vector [Z] such that satisfies the complex interval linear system C[Z]=[W]. For this, we present a new method by restricting the general solution set via applying some parameters. The numerical examples are given to show ability and reliability of the proposed method.Keywords: Complex interval vector, Complex interval linear system, Crout decomposition method
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Pages 56-67In this paper we studied the translation surfaces according to a new frame called q-frame in three dimensional Euclidean space. The curvatures of the translation surface are obtained in terms of q-frame curvatures. Finally some special cases are investigated for these surfaces.Keywords: q-frame, transation surfaces, Gauss curvature
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Pages 68-85Terrorism is generally understood to be the use of threat or extra normal violence to gain ideological reasons and personal benefit. In this paper, a mathematical modelling of terrorism with military strategies and rehabilitation of terrorists was constructed. The model is developed to control the spread of terrorist ideologies in the society and suitable to describe terrorist group. The population is divided into six compartments: $S(t)$, $I(t)$, $T(t)$, $T_L(t)$, $T_S(t)$ and $Q_T(t)$. Furthermore, the basic reproduction number, $R_0$ is also calculated if $R_0 < 1$ means the terror-organization is nearly eradicated and if $R_0 > 1$ means the number of terrorists are high where the terrorist are endemic to the population. The result of the sensitivity analysis shows that the most sensitive parameters is the recruitment pool of the terrorist from susceptible to moderate $(beta_{1})$ and terrorist move to detention facilities due to counter-terrorist activities $(b)$. The least parameter is the probability at which terrorist become militancy leaders $(kalpha)$. $(beta_{1})$ and $(b)$ are parameters counter terrorist need to be target. The finding shows that the military/dialogue strategies are to be used while military strategies alone should not be used if the number of terrorists is below a certain reproduction numberKeywords: Counter-Terrorist, Modelling, Terrorism, Dynamic, Sensitivity Analysis
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Pages 86-99In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined for frames throughout spacelike, timelike, lightlike curves. It is shown that the vector field which takes part in [17] is normal Fermi-Walker parallel by the normal Fermi-Walker derivative throughout the spacelike, timelike, and lightlike general helix. Also, we show that the Frenet frame is a normal non-rotating frame using the normal Fermi-Walker derivative. Afterward, we testified that the adapted frame is a normal non-rotating frame throughout the spacelike, timelike, and lightlike general helix.Keywords: Frenet frame, Normal Fermi-Walker derivative, Normal Non-rotating frame, Spacelike Curve, Timelike Curve
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Pages 100-123In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.Keywords: Compact linear operator, Lipschitz algebra, Pointed metric space, Weighted composition operator
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Pages 124-136This paper presents a successive approximation method (SAM) for solving a large class of optimal control problems. The proposed analytical-approximate method, successively solves the Two-Point Boundary Value Problem (TPBVP), obtained from the Pontryagin's Maximum Principle (PMP). The convergence of this method is proved and a control design algorithm with low computational complexity is presented. Through the finite number of algorithm iterations, a suboptimal control law is obtained for the optimal control problem. An illustrative example is given to demonstrate the efficiency of the proposed method.Keywords: Optimal control problem, Successive approximation method, Pontryagin's maximum principle, Suboptimal control
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Pages 137-150A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighted~slant~Toep}$-$it{Hank}$ operator is also obtained.Keywords: Weighted slant Hankel operators, Slant weighted Toeplitz operators, slant Toep-Hank operator
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Pages 151-158In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.Keywords: Univalent functions, 2(j, k)-Symmetric conjugate, Coefficient bound, Convolution