The purpose of this paper is to define the notions of convergence, Cauchy st–convergence, st–Cauchy, I –convergence and I –Cauchy for double sequences in 2–fuzzy n–normed spaces with respect to α–n–norms and ...The purpose of this paper is to define the notions of convergence, Cauchy st–convergence, st–Cauchy, I –convergence and I –Cauchy for double sequences in 2–fuzzy n–normed spaces with respect to α–n–norms and study certain classical and standard properties related to these notions.展开更多
Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the ef...Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of effluents through a sea outfall. The solutions are illustrated graphically by plotting contours of concentration, resembling snapshots of discharged effluent plumes in the far-field. Different shapes of effluent plumes are observed due to the variability of length of the step seabed, and the concentration at the step seabed is formulated to measure how much has discharged effluents dispersed into or out of the shallow coastal waters.展开更多
<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src=&qu...<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>展开更多
We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous...We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous work.Our argument is based on duality technique and direct estimation of operators.As a consequence of our result,we deduce the L^P boundedness of a class of fractional Marcinkiewicz integral operators.展开更多
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
The contact rate is defined as the average number of contacts adequate for disease transmission by an individual per unit time and it is usually assumed to be constant in time.However,in reality,the contact rate is no...The contact rate is defined as the average number of contacts adequate for disease transmission by an individual per unit time and it is usually assumed to be constant in time.However,in reality,the contact rate is not always constant throughout the year due to different factors such as population behavior,environmental factors and many others.In the case of serious diseases with a high level of infection,the population tends to reduce their contacts in the hope of reducing the risk of infection.Therofore,it is more realistic to consider it to be a function of time.In particular,the study of models with contact rates decreasing in time is well worth exploring.In this paper,an SIR model with a time-varying contact rate is considered.A new form of a contact rate that decreases in time from its initial value till it reaches a certain level and then remains constant is proposed.The proposed form includes two important parameters,which represent how far and how fast the contact rate is reduced.These two parameters are found to play important roles in disease dynamics.The existence and local stability of the equilibria of the model are analyzed.Results on the global stability of disease-free equilibrium and transcritical bifurcation are proved.Numerical simulations are presented to illustrate the theoretical results and to demonstrate the effect of the model parameters related to the behavior of the contact rate on the model dynamics.Finally,comparisons between the constant,variable contact rate and variable contact rate with delay in response cases are presented.展开更多
In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that...In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).展开更多
文摘The purpose of this paper is to define the notions of convergence, Cauchy st–convergence, st–Cauchy, I –convergence and I –Cauchy for double sequences in 2–fuzzy n–normed spaces with respect to α–n–norms and study certain classical and standard properties related to these notions.
文摘Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of effluents through a sea outfall. The solutions are illustrated graphically by plotting contours of concentration, resembling snapshots of discharged effluent plumes in the far-field. Different shapes of effluent plumes are observed due to the variability of length of the step seabed, and the concentration at the step seabed is formulated to measure how much has discharged effluents dispersed into or out of the shallow coastal waters.
文摘<span style="font-family:Verdana;">Let <img alt="" src="Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png" />be the partial symmetric semigroup on <img alt="" src="Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png" />and let <img alt="" src="Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png" />and <img alt="" src="Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt="" src="Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png" />, respectively. In this paper we investigate the cardinalities of <img alt="" src="Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png" />and <img alt="" src="Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png" />, the set idempotents of <img alt="" src="Edit_ac8237f8-83ec-4767-9029-b546377bf106.png" />and <img alt="" src="Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt="" src="Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png" />and <img alt="" src="Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png" />.</span>
文摘We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous work.Our argument is based on duality technique and direct estimation of operators.As a consequence of our result,we deduce the L^P boundedness of a class of fractional Marcinkiewicz integral operators.
文摘We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
基金Authors would like to acknowledge financial support from Sultan Qaboos University,Oman and United Arab Emirates University through the Joint Research Grant No.CL/SQU-UAEU/17/01.
文摘The contact rate is defined as the average number of contacts adequate for disease transmission by an individual per unit time and it is usually assumed to be constant in time.However,in reality,the contact rate is not always constant throughout the year due to different factors such as population behavior,environmental factors and many others.In the case of serious diseases with a high level of infection,the population tends to reduce their contacts in the hope of reducing the risk of infection.Therofore,it is more realistic to consider it to be a function of time.In particular,the study of models with contact rates decreasing in time is well worth exploring.In this paper,an SIR model with a time-varying contact rate is considered.A new form of a contact rate that decreases in time from its initial value till it reaches a certain level and then remains constant is proposed.The proposed form includes two important parameters,which represent how far and how fast the contact rate is reduced.These two parameters are found to play important roles in disease dynamics.The existence and local stability of the equilibria of the model are analyzed.Results on the global stability of disease-free equilibrium and transcritical bifurcation are proved.Numerical simulations are presented to illustrate the theoretical results and to demonstrate the effect of the model parameters related to the behavior of the contact rate on the model dynamics.Finally,comparisons between the constant,variable contact rate and variable contact rate with delay in response cases are presented.
文摘In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).
