Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d）...Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.展开更多
We prove two-Ar^λ（Ω）-weighted imbedding theorems for differential forms. These results can be used to study the weighted norms of the homotopy operator T from the Banach space LV（D, ∧^l） to the Sobolev space W^...We prove two-Ar^λ（Ω）-weighted imbedding theorems for differential forms. These results can be used to study the weighted norms of the homotopy operator T from the Banach space LV（D, ∧^l） to the Sobolev space W^1,p（D, ∧^l-1）, l = 0, 1,..., n, and to establish the weighted L^p-estimates for differential forms. Finally, we give some applications of the above results to quasiregular mappings.展开更多
The author introduces a new hypnotherapeutic technique termed “Mental Access/Somatosensory Access” (MASSA). MASSA is designed to utilize an external somatosensory stimulus in the context of hypnotherapy, based on a ...The author introduces a new hypnotherapeutic technique termed “Mental Access/Somatosensory Access” (MASSA). MASSA is designed to utilize an external somatosensory stimulus in the context of hypnotherapy, based on a Bottom-Up/Top-Down Paradigm, which complements and mutually reinforces hypnotic inductions by using imbedded suggestions. The intervention’s algorithm includes a combination of real-time stimulation through one of the following somatosensory modalities: sensorimotor activation of the palms, visual, auditory, vibration, thermal, olfaction or oropharyngeal. These modalities are accompanied by guided hypnotic dissociation and suggestions. Somatosensory stimulation amplifies patients’ engagement in the procedure, focusing their attention on a stimulus and on the hypnotic experience during the intervention. A stream of closed questions with imbedded suggestions, presented by the therapist, is designed using suggestive presuppositions, termed by the author “The Create and Verify Principle” (CVP). This principle facilitates effective pacing and helps transform patients’ sensory and mental experiences. Imbedded suggestions followed by real-time stimulation, maintain a focus on the somatosensory content, boost the hypnotic experience, and gradually combine awareness of the somatosensory stimulation experience (Bottom-Up regulation) with memory, imagination, emotions and meanings, for mental access of resources and adaptive coping (Top-Down regulation). In the first part of this article, the author briefly introduces the neurophysiological mechanism behind the suggestive, somatosensory, attention-management intervention and provides an example of a basic algorithm of the MASSA technique. The second part includes clinical samples with scripts of successfully treated patients, who experienced tension headache, psychogenic balance disorder, tinnitus. .展开更多
Hilbert space method is applied to a class of semilinear second_order elliptic boundary value problems and the existence of solutions is obtained with some restrictions.
In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the ...In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T>0.展开更多
Several contradictions inherent for relativistic dynamics get evident in the case of mechanical systems of cyclic type. In the present paper a version of situation taking place in the moving belt transmission is exami...Several contradictions inherent for relativistic dynamics get evident in the case of mechanical systems of cyclic type. In the present paper a version of situation taking place in the moving belt transmission is examined. It is shown that non-Euclidean intrinsic geometry, appearing during acceleration, does not abolish the real paradox in this mechanism. An unavoidable discrepancy between Special and General relativities is established. So, the very existence of wormholes becomes a moot point.展开更多
In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an ele...In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).展开更多
In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary...In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacje problems are given.展开更多
In this note we use the scalar field K(=R or C)and always suppose that Γ is an infinite index set and Ω is a compact Hausdorff space. All the keywords (except the last one) are from Ref. [1].
Investigates three various algorithms for computation and implementation of general limit representations of generalized inverses. Introduction and preliminaries; Details of the generalized imbedding method; Limit rep...Investigates three various algorithms for computation and implementation of general limit representations of generalized inverses. Introduction and preliminaries; Details of the generalized imbedding method; Limit representation and orthogonal systems.展开更多
基金Supported by the Natural Science Foundation of China (10971251)
文摘Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.
基金The research supported by National Natural Science Foundation of China (A0324610)Scientific Research Foundation of Hebei Polytechnic University (200520).
文摘We prove two-Ar^λ（Ω）-weighted imbedding theorems for differential forms. These results can be used to study the weighted norms of the homotopy operator T from the Banach space LV（D, ∧^l） to the Sobolev space W^1,p（D, ∧^l-1）, l = 0, 1,..., n, and to establish the weighted L^p-estimates for differential forms. Finally, we give some applications of the above results to quasiregular mappings.
文摘The author introduces a new hypnotherapeutic technique termed “Mental Access/Somatosensory Access” (MASSA). MASSA is designed to utilize an external somatosensory stimulus in the context of hypnotherapy, based on a Bottom-Up/Top-Down Paradigm, which complements and mutually reinforces hypnotic inductions by using imbedded suggestions. The intervention’s algorithm includes a combination of real-time stimulation through one of the following somatosensory modalities: sensorimotor activation of the palms, visual, auditory, vibration, thermal, olfaction or oropharyngeal. These modalities are accompanied by guided hypnotic dissociation and suggestions. Somatosensory stimulation amplifies patients’ engagement in the procedure, focusing their attention on a stimulus and on the hypnotic experience during the intervention. A stream of closed questions with imbedded suggestions, presented by the therapist, is designed using suggestive presuppositions, termed by the author “The Create and Verify Principle” (CVP). This principle facilitates effective pacing and helps transform patients’ sensory and mental experiences. Imbedded suggestions followed by real-time stimulation, maintain a focus on the somatosensory content, boost the hypnotic experience, and gradually combine awareness of the somatosensory stimulation experience (Bottom-Up regulation) with memory, imagination, emotions and meanings, for mental access of resources and adaptive coping (Top-Down regulation). In the first part of this article, the author briefly introduces the neurophysiological mechanism behind the suggestive, somatosensory, attention-management intervention and provides an example of a basic algorithm of the MASSA technique. The second part includes clinical samples with scripts of successfully treated patients, who experienced tension headache, psychogenic balance disorder, tinnitus. .
文摘Hilbert space method is applied to a class of semilinear second_order elliptic boundary value problems and the existence of solutions is obtained with some restrictions.
文摘In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T>0.
文摘Several contradictions inherent for relativistic dynamics get evident in the case of mechanical systems of cyclic type. In the present paper a version of situation taking place in the moving belt transmission is examined. It is shown that non-Euclidean intrinsic geometry, appearing during acceleration, does not abolish the real paradox in this mechanism. An unavoidable discrepancy between Special and General relativities is established. So, the very existence of wormholes becomes a moot point.
文摘In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).
文摘In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacje problems are given.
文摘In this note we use the scalar field K(=R or C)and always suppose that Γ is an infinite index set and Ω is a compact Hausdorff space. All the keywords (except the last one) are from Ref. [1].
文摘Investigates three various algorithms for computation and implementation of general limit representations of generalized inverses. Introduction and preliminaries; Details of the generalized imbedding method; Limit representation and orthogonal systems.
