We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.
The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-norm...The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.展开更多
We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isome...We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.展开更多
In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the co...In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.展开更多
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
The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space....The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.展开更多
The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing t...The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing the Cardox tube.However,there is a lack of impact pressure testing of disposable tubes under real working conditions,selection of gas explosion design parameters,and systematic analysis of blasting vibration.This limitation has constrained the widespread application of disposable fracturing tubes in engineering.A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted.The rock-breaking effect of varying hole spacing parameters in the EFLCO_(2)design was analyzed,and a systematic study was carried out on the vibration peak value,frequency,and energy characteristics.The results show that(1)the pressure distribution characteristics,stress peak value,and duration in the disposable tubes are different from those of Cardox tubes,which show multi-peak distribution,low-pressure peak value,and short duration.The correlation between the pressure in the disposable tube,filling pressure,and liquid CO_(2)weight is established,and a theoretical calculation method for the borehole wall pressure is proposed;(2)The hole spacing in rocks of different hardness is suggested;and(3)At the same scale distance,the peak particle velocity(PPV)caused by EFLCO_(2)(PPVCO_(2))is significantly smaller than that caused by blasting(PPVexplosive).The ratio of PPVexplosive to PPVCO_(2)is a power function related to scale distance,and a distance-related zonality exist in this relationship.The frequency composition of the vibration signal caused by EFLCO_(2)is relatively simple with a narrow frequency band.Its PPV and energy are mainly concentrated in the low-frequency band.This research contributes to the optimization of disposable fracturing tubes,gas explosion design,and vibration hazard control.展开更多
In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
文摘We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.
文摘The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.
文摘We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.
文摘In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.
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The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.
基金financially supported by the National Key R&D Program of China(Grant No.2020YFA0711802)the Wuhan Science and Technology Bureau of China(Grant No.2023020201010081)the National Nature Science Foundation of China(Grant No.U22A20239).
文摘The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing the Cardox tube.However,there is a lack of impact pressure testing of disposable tubes under real working conditions,selection of gas explosion design parameters,and systematic analysis of blasting vibration.This limitation has constrained the widespread application of disposable fracturing tubes in engineering.A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted.The rock-breaking effect of varying hole spacing parameters in the EFLCO_(2)design was analyzed,and a systematic study was carried out on the vibration peak value,frequency,and energy characteristics.The results show that(1)the pressure distribution characteristics,stress peak value,and duration in the disposable tubes are different from those of Cardox tubes,which show multi-peak distribution,low-pressure peak value,and short duration.The correlation between the pressure in the disposable tube,filling pressure,and liquid CO_(2)weight is established,and a theoretical calculation method for the borehole wall pressure is proposed;(2)The hole spacing in rocks of different hardness is suggested;and(3)At the same scale distance,the peak particle velocity(PPV)caused by EFLCO_(2)(PPVCO_(2))is significantly smaller than that caused by blasting(PPVexplosive).The ratio of PPVexplosive to PPVCO_(2)is a power function related to scale distance,and a distance-related zonality exist in this relationship.The frequency composition of the vibration signal caused by EFLCO_(2)is relatively simple with a narrow frequency band.Its PPV and energy are mainly concentrated in the low-frequency band.This research contributes to the optimization of disposable fracturing tubes,gas explosion design,and vibration hazard control.
文摘In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.