In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presenta...In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presentations of a group, i.e. different ways of expressing its elements and operations. We have also applied this algorithm to a subgroup generated H by G;where we obtained a table of the subgroup, three tables of relators including: Table of the relator aaaa;Table of the relator abab;Table of the relator bbb and a multiplication table aa'bb'. Once the algorithm is complete, the unit of H in G is 6. We have explicitly obtained a homomorphism of G in the group of permutations of H/G which is isomorphic to G6;where we have noticed that it is injective: in fact, an element of the nucleus belongs to the intersection of the xHx−1for x∈G, in particular, it belongs to H;on the other hand, the image of H in G6 is of order 4, so the nucleus is reduced to the neutral element.展开更多
We study the structure of Bernstein's first summable operators and show that they con- verge uniformly to continuons functions on the special real orthogonal group SO(n)in this paper.In addition,we have also discu...We study the structure of Bernstein's first summable operators and show that they con- verge uniformly to continuons functions on the special real orthogonal group SO(n)in this paper.In addition,we have also discussed the approximation degree to a class of function Lipα(0<α≤1)on SO(n).展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
The technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P<SUP>2</SUP>, Q<SUP>2</SUP&...The technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P<SUP>2</SUP>, Q<SUP>2</SUP>, PQ + QP) to those of the basis operators (a<SUP>2</SUP>, a<SUP>?2</SUP>, a<SUP>?</SUP>a). The coherent state representation of unitary squeezing operators in the factorized form and their normal product form are thus derived. The squeezing engendered by operators of the general form is also obtained.展开更多
In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodyna...In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.展开更多
Objective To introduce an operation procedure and evaluate the continence diversion results of the modified ureterosigmoidostomy after radical cystectomy. Methods Fourteen cases of bladder cancer or prostate carcin...Objective To introduce an operation procedure and evaluate the continence diversion results of the modified ureterosigmoidostomy after radical cystectomy. Methods Fourteen cases of bladder cancer or prostate carcinoma were operated on with modified Sigma pouch from Feb, 1998 to Dec, 1999. A longitudinal incision about 25 cm on the sigmoid wall was done to form a low pressure pouch. The vertex of the new pouch was fixed to sacrum. Both ends of ureters were anastomosed side to side and to form a big nipple and inserted into the top of pouch for 2 to 3 centimeters.Results It took about sixty five minutes to create a new low pressure pouch after radical cystectomy. Early complication of was found in two cases postoperatively, and cured with temporary colonostomy. Hydronephrosis and hypokalemia in one patient were cured by percutaneous anterograde ureter dilatation with balloon and oral replacement of potassium salt. All patients displayed urinary continence. No symptomatic renal infection or hypercholoraemic acidosis occurred. Conclusion Modified ureterosigmoidostomy is a safe procedure of urinary diversion and provides a big volume, low intravesical pressure pouch. The patients are free from the troublesome urine bag, intermittert catheterization, and upper urinary tracts are protected effectively. The quality of life is satisfied.展开更多
IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub&g...IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub> group of unitary operators on a Hilbert space if and only if it is skew-adjoint. This result has been applied extensively to linear partial differential equations （PDEs） with a law of conservation. Hille [2] then discovered the generation theorem of the Hille-Yosida type for a C<sub>0</sub> group on a Banach space. There are also some conditions under which a C<sub>0</sub> semigroup on a Banach space can be embedded in a C<sub>0</sub> group. We refer the readers to ref. [3] for details of the results mentioned above.展开更多
This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is ...This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.展开更多
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the g...We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.展开更多
We are pleased to announce that from 2012 the name of the Journal of Mathematical Re- search and Exposition （JMRE） will be changed to Journal of Mathematical Research with Applications （JMRA） with ISSN changed fro...We are pleased to announce that from 2012 the name of the Journal of Mathematical Re- search and Exposition （JMRE） will be changed to Journal of Mathematical Research with Applications （JMRA） with ISSN changed from 1000-341X to 2095-2651, and CN from 21-1208/O1 to 21-1579/O1.展开更多
文摘In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presentations of a group, i.e. different ways of expressing its elements and operations. We have also applied this algorithm to a subgroup generated H by G;where we obtained a table of the subgroup, three tables of relators including: Table of the relator aaaa;Table of the relator abab;Table of the relator bbb and a multiplication table aa'bb'. Once the algorithm is complete, the unit of H in G is 6. We have explicitly obtained a homomorphism of G in the group of permutations of H/G which is isomorphic to G6;where we have noticed that it is injective: in fact, an element of the nucleus belongs to the intersection of the xHx−1for x∈G, in particular, it belongs to H;on the other hand, the image of H in G6 is of order 4, so the nucleus is reduced to the neutral element.
文摘We study the structure of Bernstein's first summable operators and show that they con- verge uniformly to continuons functions on the special real orthogonal group SO(n)in this paper.In addition,we have also discussed the approximation degree to a class of function Lipα(0<α≤1)on SO(n).
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
文摘The technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P<SUP>2</SUP>, Q<SUP>2</SUP>, PQ + QP) to those of the basis operators (a<SUP>2</SUP>, a<SUP>?2</SUP>, a<SUP>?</SUP>a). The coherent state representation of unitary squeezing operators in the factorized form and their normal product form are thus derived. The squeezing engendered by operators of the general form is also obtained.
基金Kampachi Farms LLC for their support to complete this work and for all the technical information provided to complete the numerical model
文摘In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.
文摘Objective To introduce an operation procedure and evaluate the continence diversion results of the modified ureterosigmoidostomy after radical cystectomy. Methods Fourteen cases of bladder cancer or prostate carcinoma were operated on with modified Sigma pouch from Feb, 1998 to Dec, 1999. A longitudinal incision about 25 cm on the sigmoid wall was done to form a low pressure pouch. The vertex of the new pouch was fixed to sacrum. Both ends of ureters were anastomosed side to side and to form a big nipple and inserted into the top of pouch for 2 to 3 centimeters.Results It took about sixty five minutes to create a new low pressure pouch after radical cystectomy. Early complication of was found in two cases postoperatively, and cured with temporary colonostomy. Hydronephrosis and hypokalemia in one patient were cured by percutaneous anterograde ureter dilatation with balloon and oral replacement of potassium salt. All patients displayed urinary continence. No symptomatic renal infection or hypercholoraemic acidosis occurred. Conclusion Modified ureterosigmoidostomy is a safe procedure of urinary diversion and provides a big volume, low intravesical pressure pouch. The patients are free from the troublesome urine bag, intermittert catheterization, and upper urinary tracts are protected effectively. The quality of life is satisfied.
文摘IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub> group of unitary operators on a Hilbert space if and only if it is skew-adjoint. This result has been applied extensively to linear partial differential equations （PDEs） with a law of conservation. Hille [2] then discovered the generation theorem of the Hille-Yosida type for a C<sub>0</sub> group on a Banach space. There are also some conditions under which a C<sub>0</sub> semigroup on a Banach space can be embedded in a C<sub>0</sub> group. We refer the readers to ref. [3] for details of the results mentioned above.
基金supported by Grant-in-Aid for Young Scientists(B)(Grant No.23740106)
文摘This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
文摘We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.
文摘We are pleased to announce that from 2012 the name of the Journal of Mathematical Re- search and Exposition （JMRE） will be changed to Journal of Mathematical Research with Applications （JMRA） with ISSN changed from 1000-341X to 2095-2651, and CN from 21-1208/O1 to 21-1579/O1.
