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
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
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.
OBJECTIVE To summarize a common pathogenefic condition, the pathologic characteristics shown in frozen section and our experience utilizing 2 different common thyroid diseases （TD）. diagnostic methods in cases of ME...OBJECTIVE To summarize a common pathogenefic condition, the pathologic characteristics shown in frozen section and our experience utilizing 2 different common thyroid diseases （TD）. diagnostic methods in cases of METHODS Data from 638 cases with frozen sections from thyroid tissue were retrospectively analyzed. The intraoperative frozen sections of the patients and postoperative diagnostic results of routine paraffin sections were compared. RESULTS In the 683 patients, the gender ratio of females to males was 2.64 ： 1, and the ratio between the patients with nodular goiter （NG） and the patients with thyroid adenoma was 1.5 ： 1. The oldest age group of patients with thyroid cancer （TC） ranged from 40 to 49 years. Frozen section pathologic examination has been employed more and more in the diagnosis of thyroid diseases, and the detection rate of TC has increased year by year, i.e., the rate increased to 6.45%, 7.58%, 14.55% and 16.57%, respectively, in 2005, 2006, 2007 and 2008. Thyroid papillary carcinoma （TPC） was the most commonly seen malignant tumor of the thyroid （MTT）, which accounted for approximately 94.8% of MTTs and 11.44% of the total TDs. Micropapillary carcinoma accounted for 27.4% of TPC, and multifocal carcinomas accounted for 15.58% of TCs. Many of the TCs （19.48%） were complicated by benign diseases such as adenoma, NG and thyroiditis. The coincidence rate of diagnoses made by frozen section and paraffin embedding for thyroid disease was 98.59%. Calcification was rather common in NG and TPC, and there were significant differences in psammoma bodies （PMB） between the calcifications of TPC and NG （P 〈 0.01）. CONCLUSION TPC ranks first in the incidence of MTTs and accounts for 94.8% of all MTTs. About 1/4 of TPCs are micropapillary carcinoma, while 1/5 are accompanied by benign disease, such as adenorna, NG and thyroiditis. PMB are of importance and of significance in the diagnosis of TPC.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
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
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
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OBJECTIVE To summarize a common pathogenefic condition, the pathologic characteristics shown in frozen section and our experience utilizing 2 different common thyroid diseases （TD）. diagnostic methods in cases of METHODS Data from 638 cases with frozen sections from thyroid tissue were retrospectively analyzed. The intraoperative frozen sections of the patients and postoperative diagnostic results of routine paraffin sections were compared. RESULTS In the 683 patients, the gender ratio of females to males was 2.64 ： 1, and the ratio between the patients with nodular goiter （NG） and the patients with thyroid adenoma was 1.5 ： 1. The oldest age group of patients with thyroid cancer （TC） ranged from 40 to 49 years. Frozen section pathologic examination has been employed more and more in the diagnosis of thyroid diseases, and the detection rate of TC has increased year by year, i.e., the rate increased to 6.45%, 7.58%, 14.55% and 16.57%, respectively, in 2005, 2006, 2007 and 2008. Thyroid papillary carcinoma （TPC） was the most commonly seen malignant tumor of the thyroid （MTT）, which accounted for approximately 94.8% of MTTs and 11.44% of the total TDs. Micropapillary carcinoma accounted for 27.4% of TPC, and multifocal carcinomas accounted for 15.58% of TCs. Many of the TCs （19.48%） were complicated by benign diseases such as adenoma, NG and thyroiditis. The coincidence rate of diagnoses made by frozen section and paraffin embedding for thyroid disease was 98.59%. Calcification was rather common in NG and TPC, and there were significant differences in psammoma bodies （PMB） between the calcifications of TPC and NG （P 〈 0.01）. CONCLUSION TPC ranks first in the incidence of MTTs and accounts for 94.8% of all MTTs. About 1/4 of TPCs are micropapillary carcinoma, while 1/5 are accompanied by benign disease, such as adenorna, NG and thyroiditis. PMB are of importance and of significance in the diagnosis of TPC.
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)).
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.
