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摘要:In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended....
摘要:A canonical p-adic Frobenius lift is defined in the context of p-adic numbers, viewed as deformations of the corresponding finite field. Applications to p-adic periods are considered, including to the classical Euler gamma and beta functions and their p-adic analogues, from a cohomological point of view. Connections between various methods for computing scattering amplitudes are related to the moduli space problem and period domains....
[期刊论文] Siqi Tao
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2018年 4期
摘要:In this paper, we first reformulate the max-min dispersion problem as a style="font-family:Verdana;"> saddle-point problem. Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem. Then we propose the saddle-point problem to be solved by an adaptive custom proximal point algorithm. Numerical results show that the proposed algorithm is efficient....
摘要:Finite fields form an important chapter in abstract algebra, and mathematics in general, yet the traditional expositions, part of Abstract Algebra courses, focus on the axiomatic presentation, while Ramification Theory in Algebraic Number Theory, making a suited topic for their applications, is usually a separated course. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a much larger audience, and bridging the above mentioned gap. Such lattice models of finite fields provide a good basis for later developing their study in a more concrete way, including decomposition of primes in number fields, Frobenius elements, and Frobenius lifts, allowing to approach more advanced topics, such as Artin reciprocity law and Weil Conjectures, while keeping the exposition to the concrete level of familiar number systems. Examples are provided, intended for an undergraduate audience in the first place....
摘要:The original online version of this article (Issa Allassane Kaboye, Bazanfaré Mahaman style="font-size:10pt;font-family:""> style="font-family:Verdana;">(2016) Manifolds with Bakry-Emery Ricci Curvature bounded below 6, 754-764 style="font-family:Verdana;">. style="font-size:10pt;font-family:""> style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;">http://dx.doi.org/ style="font-family:Verdana;font-size:12px;"> style="font-family:Verdana;font-size:12px;">10.4236/apm.2016.611061 style="font-size:10pt;font-family:""> style="font-family:Verdana;">unfortunately contains a mistake. The author wishes to correct the errors....
[期刊论文] Yijian Ge
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2019年 10期
摘要:In this paper, we study the existence of solution for some style="white-space:nowrap;">p(x)-polyharmonic Kirchhoff equations. The latter is allowed to vanish at the origin (degenerate case). Firstly, we study the existence of solutions of approximate equations. Secondly, we prove the existence of the solutions of the original equation. The main tool is the Schauder’s Theorem....
摘要:We are dealing with domains of the complex plane which are not symmetric in common sense, but support fixed point free antianalytic involutions. They are fundamental domains of different classes of analytic functions and the respective involutions are obtained by composing their canonical projections onto the complex plane with the simplest antianalytic involution of the Riemann sphere. What we obtain are hidden symmetries of the complex plane. The list given here of these domains is far from exhaustive....
[期刊论文] Rong Hu
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2019年 10期
摘要:Different function spaces have certain inclusion or equivalence relations. In this paper, the author introduces a class of M style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:"font-size:13px;white-space:normal;background-color:#FFFFFF;">öbius-invariant Banach spaces style="font-family:Tahoma, sans-serif;font-size:9pt;">QK,0 (p,q) of analytic function on the unit ball of style="font-family:Tahoma, sans-serif;font-size:9pt;">Cn, where style="font-family:Tahoma, sans-serif;font-size:9pt;">K:(0,∞)→[0,∞) are non-decreasing functions and lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">0 lang="EN-US" style="font-size:9pt;font-family:Verdana, sans-serif;background:white;">< lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">P lang="EN-US" style="font-size:9pt;font-family:Verdana, sans-serif;background:white;">< lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">∞, p/2 lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">-n-1 lang="EN-US" style="font-size:9pt;font-family:Verdana, sans-serif;background:white;">< lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">q lang="EN-US" style="font-size:9pt;font-family:Verdana, sans-serif;background:white;">< lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">∞, studies the inclusion relations between style="font-family:Tahoma, sans-serif;font-size:9pt;">QK,0 (p,q) and a class of lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">B0 lang="EN-US" style="font-size:9pt;font-family:" color:#666666;"="">α lang="EN-US" style="font-size:9pt;"> style="font-family:'Tahoma, sans-serif';"> spaces which was known before, and concludes that style="font-family:Tahoma, sans-serif;font-size:9pt;">QK,0 (p,q) is a subspace of lang="EN-US" style="font-size:9pt;font-family:Tahoma, sans-serif;">B0 lang="EN-US" style="font-size:9...
摘要:In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations....
摘要:The purpose of this article is to formulate Bayesian updating from dynamical viewpoint. We prove that Bayesian updating for population mean vectors of multivariate normal distributions can be expressed as an affine symplectic transformation on a phase space with the canonical symplectic structure....
摘要:In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introduction of special intervals between square of prime numbers that I call silver intervals src="Edit_9a37e905-0ca3-49fc-8b02-666964a602f4.bmp" alt="" />. And I make introduction of another also new mathematic phenomenon of logical proposition In mathematics nothing happens without reason” for which I use the ancient Greek term “catholic information”. From the theorem of prime numbers we know that the expected multitude of prime numbers in an interval src="Edit_fa2862c5-f8db-440c-bfe0-15828192c782.bmp" alt="" /> is given by formula src="Edit_c78aa576-b27d-4244-85ec-4fc1cd19392f.png" alt="" /> considering that interval as a continuous distribution of real numbers that represents an elementary natural numbers interval. From that we find that in the elementary interval src="Edit_a65513fd-86f9-43a2-9788-a2962f42bc74.png" alt="" /> around of a natural number ν we easily get by dx=1 the probability src="Edit_d4091cc5-951e-449c-ae3b-cc479b4173ff.png" alt="" /> that has the ν to be a prime number. From the last formula one can see that the second part src="Edit_a90504e5-42f6-4bb7-9606-2c0cc4c63805.bmp" alt="" /> of formula (4.18) is absolutely in agreement with the above theorem of prime numbers. But the benefit of the (4.18) is that this formula enables correct calculations in set N on finding the multitude of twin prime numbers, in contrary of the above logarithmic relation which is an approximation and must tend to be correct as ν tends to infinity. Using the relationship (4.18) we calculate here the multitude of twins in N, concluding that this multitude tends to infinite. But for the validity of the computation, the distribution of the primes in a random silver interval src="Edit_b0610670-aaea-43e0-a56c-635fd1919ee1.bmp" alt="" /> is examined, proving on the basis of catholic information that the density of primes in the same random silver interval src="Edit_91f64412-5458-4098-82f6-9570da456f8f.bmp" alt="" /> is statistically constant. Below, in introduction, we will define this concept of “catholic information” stems of “information theory” [1] and it is defined to use only general forms in set N, because these represent the set N and not finite parts of it. This concept must be correlated to Riemann Hypothesis....
摘要:In this paper, an isogeometric error estimate for transport equation is obtained in 2D to prove the convergence of isogeometric method. The result that we have obtained, generalizes Ern result, got in finite elements method. For the time discretization, the two stage Heun scheme is used to prove this result. For a polynomial of degree k style="color:#333333;font-family:" font-size:14px;white-space:normal;background-color:#ffffff;"="">≥1, the order of convergence in space is 2 and in time is src="Edit_b9824df7-6a7e-4366-98fa-9fca5e9bc790.bmp" alt="" />....
摘要:In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. A possible generalization of L style="white-space:nowrap;"> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:"font-size:13px;white-space:normal;background-color:#FFFFFF;">öb’s theorem is considered. Main results are: 1) src="Edit_23766ff8-f62e-4cf7-bf5d-bb30af825eb8.bmp" alt="" />, 2) src="Edit_38c38a8a-6aee-4fd3-838e-4b1a1a6f1189.bmp" alt="" />, 3) src="Edit_39195e43-7564-4883-aa10-997f7cbe0604.bmp" alt="" />, 4) src="Edit_5614f588-7c59-445e-892c-44e626f6f6c3.bmp" alt="" />, 5) let k be inaccessible cardinal then src="Edit_ed6e297d-4e88-4e1b-9c76-1b5d668e20da.bmp" alt="" />....
[期刊论文] Jeff Brown
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2019年 09期
摘要:Let E be a toric fibration arising from symplectic reduction of a direct sum of complex line bundles over (almost) K style="white-space:nowrap;"> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:" font-size:13px;white-space:normal;background-color:#ffffff;"=""> style="color:#333333;font-family:"font-size:13px;white-space:normal;background-color:#FFFFFF;">ähler base B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let La be convex line bundles over B, Aa smooth divisors of B arising as the zero loci of generic sections of style="white-space:nowrap;">La , and src="Edit_170b9ffb-960a-4baa-8267-393b7b206331.bmp" alt="" /> a particular fixed-point section of E. Further assume the {Aa} to be mutually disjoint. The manifold src="Edit_04f8d5f6-a5b4-4ea5-a023-053c02222681.bmp" alt="" /> is a new manifold with tautological line bundles over new projective spaces in the geometry, where previously there was a simpler vector bundle in the given local geometry (Section 1.5). Thus, we compute genus-0 Gromov-Witten invariants of src="Edit_cf4322b0-67d7-4ef3-b3e3-71c6d2734535.bmp" alt="" /> in terms of genus-0 Gromov-Witten invariants of B and of style="white-space:nowrap;">{Aa}, the matrix used for the symplectic reduction description of the fiber of the toric fibration E style="white-space:nowrap;">→B, and the restriction maps src="Edit_d01212c2-e85d-4dee-850a-7f59761730c1.bmp" alt="" />. The proofs utilize the fixed-point localization technique describing the geometry of src="Edit_8f4a28a8-4e6c-4586-97c6-513238e4b3e8.bmp" alt="" /> and its genus-0 Gromov-Witten theory, as well as the Quantum Lefschetz theorem relating the genus-0 Gromov-Witten theory of A with that of B....
摘要:The notion of the holomorphic curvature for a Complex Finsler space (M,F) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. This paper is about the fundamental metric tensor, inverse tensor and as a special approach of the pull-back bundle is devoted to obtaining the holomorphic curvature of Complex Finsler Square metrics. Further, it proved that it is not a weakly K style="color:#333333;font-family:"font-size:13px;white-space:normal;background-color:#FFFFFF;">ähler....
摘要:A recent literature on qualitative analysis has shown that its successful application in testing the consistency of the sign patterns of a proposed structure and an estimated reduced form was far less restricted than a previous literature had proposed. A frequent example used in this demonstration was the qualitative analysis of Klein’s Model I. For this, the proposed structural sign pattern was falsified by the sign pattern of the estimated reduced form. As a result, the subsequent application two-stage least squares would always find quantifications of the structure that could not possibly have resulted in the sign pattern of the estimated reduced form. We view this result as a diagnostic calling for further analysis. We show that the Klein model fails standard over identification tests. We make modest amendments to the model that resolves this problem but find that the resulting estimated reduced form still falsifies the structure, calling for further developmental effort. Our point is that qualitative falsification should be viewed as a diagnostic in developing a model, rather than a criterion for entirely dismissing the model....
摘要:In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set src="Edit_4271333c-7870-4d19-a9c2-699582f92280.bmp" alt="" />. Let us denote it by src="Edit_251aceee-2696-4b54-9267-6ddb5771bd7e.bmp" alt="" />. Actually, in the same reference, it has been also defined the generating and relator sets for src="Edit_0709490c-2c25-4a71-b7e8-cd30e9be0a69.bmp" alt="" />, and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s)....
摘要:The speed of China’s economic development is gradually accelerating, and the demand for energy is also constantly increasing, especially the demand for coal. In order to reveal whether the coal imports have an impact on China’s economic development, this paper constructs the VAR(6) model by selecting the quarterly data of coal imports (CIV) and gross domestic product (GDP) from 2002 to 2017, performing ADF (Augmented Dickey-Fuller) stationarity test and Johansen cointegration test. It shows that there is a long-term stable equilibrium relationship between coal imports and GDP. Then the impulse response function is used to obtain the relationship between coal imports and GDP. It is found that the impact of coal imports on GDP is greater than the impact of GDP on coal imports....
[期刊论文] Baoqin Chen
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2019年 07期
摘要:This paper is to study the unicity of transcendental meromorphic solutions to some nonlinear difference equations. Let src="Edit_a93a5d6e-8784-42a3-8505-63a411df431f.bmp" alt="" /> be a nonzero rational function. Consider the uniqueness of transcendental meromorphic solutions to some nonlinear difference equations of the form src="Edit_9a3b22ca-428e-4b98-833c-60346c21287c.bmp" alt="" />. For two finite order transcendental meromorphic solutions of the equation above, it shows that they are almost equal to each other except for a nonconstant factor, if they have the same zeros and poles counting multiplicities, when src="Edit_dcbaa877-ba9f-44df-9033-6b1e818ac8cc.bmp" alt="" />. Two relative results are proved, and examples to show sharpness of our results are provided....
摘要:In this paper we give an algorithm for polignac numbers. That algorithm is also the base of the proof of the de Polignac's conjecture. The examples of the application present algorithm for twin, cousin, and sexy primes are included....
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