In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c...In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.展开更多
In this paper we are concerned with the oscillation criteria of second order non-linear homogeneous differential equation. Example have been given to illustrate the results.
In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Trans...In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.展开更多
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
A topographic target light scattering-differential optical absorption spectroscopy(ToTaL-DOAS) system is developed for measuring average concentrations along a known optical path and studying surface-near distribution...A topographic target light scattering-differential optical absorption spectroscopy(ToTaL-DOAS) system is developed for measuring average concentrations along a known optical path and studying surface-near distributions of atmospheric trace gases.The telescope of the ToTaL-DOAS system points to targets which are located at known distances from the measurement device and illuminated by sunlight.Average concentrations with high spatial resolution can be retrieved by receiving sunlight reflected from the targets.A filed measurement of NO2 concentration is performed with the ToTaL-DOAS system in Shijiazhuang in the autumn of 2011.The measurement data are compared with concentrations measured by the point monitoring technique at the same site.The results show that the ToTaL-DOAS system is sensitive to the variation of NO2 concentrations along the optical path.展开更多
In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct x Cxn. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near ...In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct x Cxn. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct x Cxn.展开更多
A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The m...A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.展开更多
We present variation patterns of trace elements within different sequences of the Ediacaran Doushantuo Formation(DST,635-551 million years ago),and inside the cells of the earliest differentiated multicellular eukaryo...We present variation patterns of trace elements within different sequences of the Ediacaran Doushantuo Formation(DST,635-551 million years ago),and inside the cells of the earliest differentiated multicellular eukaryotic fossils of the Weng'an biota in the Weng'an County of Guizhou Province.The results showed that selenium is the most enriched and significantly varied trace element among the 22 trace elements throughout the DST,followed by arsenic.The highest selenium and arsenic content sequences are consistent with the first appeared sequence of the earliest differentiated multicellular eukaryotic fossils Megasphaera at the middle to upper parts of the DST.Nanoman secondary ion mass spectrometry analyses show that selenium and arsenic have an inhomogeneous and punctate distribution in the nucleus and cytoplasm.The nucleus has anomalously enriched levels of selenium and arsenic among the organelles.The selenium and arsenic concentrations exhibit a positive correlation with the diversity of fossilized Megasphaera.These new findings give us a clue that the anomalous enrichment of selenium and arsenic might contributes to the cell differentiation in Ediacaran Doushantuo period.展开更多
This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation contain...This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.展开更多
In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functions F(x)=x d over field GF(2 n), with W(d)=n-1, have desirable cryptographic properties. Therefore we gen...In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functions F(x)=x d over field GF(2 n), with W(d)=n-1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion,any order propagation criteria and any order correlation immunity.展开更多
文摘In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.
文摘In this paper we are concerned with the oscillation criteria of second order non-linear homogeneous differential equation. Example have been given to illustrate the results.
文摘In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.
文摘There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
基金Project supported by the National High Technology Research and Development of China (Grant No.2009AA063006)the National Natural Science Foundation of China (Grant No. 40905010)the Special Project of Environmental Nonprofit Industry Research,China (Grant No. 201109007)
文摘A topographic target light scattering-differential optical absorption spectroscopy(ToTaL-DOAS) system is developed for measuring average concentrations along a known optical path and studying surface-near distributions of atmospheric trace gases.The telescope of the ToTaL-DOAS system points to targets which are located at known distances from the measurement device and illuminated by sunlight.Average concentrations with high spatial resolution can be retrieved by receiving sunlight reflected from the targets.A filed measurement of NO2 concentration is performed with the ToTaL-DOAS system in Shijiazhuang in the autumn of 2011.The measurement data are compared with concentrations measured by the point monitoring technique at the same site.The results show that the ToTaL-DOAS system is sensitive to the variation of NO2 concentrations along the optical path.
文摘In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct x Cxn. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct x Cxn.
文摘A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.
基金supported by the National Natural Science Foundation of China(Grant Nos.41172310 and 41877299)。
文摘We present variation patterns of trace elements within different sequences of the Ediacaran Doushantuo Formation(DST,635-551 million years ago),and inside the cells of the earliest differentiated multicellular eukaryotic fossils of the Weng'an biota in the Weng'an County of Guizhou Province.The results showed that selenium is the most enriched and significantly varied trace element among the 22 trace elements throughout the DST,followed by arsenic.The highest selenium and arsenic content sequences are consistent with the first appeared sequence of the earliest differentiated multicellular eukaryotic fossils Megasphaera at the middle to upper parts of the DST.Nanoman secondary ion mass spectrometry analyses show that selenium and arsenic have an inhomogeneous and punctate distribution in the nucleus and cytoplasm.The nucleus has anomalously enriched levels of selenium and arsenic among the organelles.The selenium and arsenic concentrations exhibit a positive correlation with the diversity of fossilized Megasphaera.These new findings give us a clue that the anomalous enrichment of selenium and arsenic might contributes to the cell differentiation in Ediacaran Doushantuo period.
文摘This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.
文摘In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functions F(x)=x d over field GF(2 n), with W(d)=n-1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion,any order propagation criteria and any order correlation immunity.
