Through the empirical research on the teaching of undergraduate professional introduction courses,the teaching experience of similar high-quality courses is refined.Based on modern educational technology,the innovativ...Through the empirical research on the teaching of undergraduate professional introduction courses,the teaching experience of similar high-quality courses is refined.Based on modern educational technology,the innovative thinking of similar course teaching is explored.By establishing a teaching community to facilitate multi-dimensional collaboration,this approach overcomes the constraints of time and space,effectively integrates teaching resources,and enhances the scientific rigor,standardization,and effectiveness of course instruction.As a result,the educational impact of professional introduction courses is continuously optimized.展开更多
The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction con...The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.展开更多
Mobile Ad Hoc Network(MANET)is a group of node that would interrelate among each other through onemulti-hop wireless link,wherein the nodes were able to move in response to sudden modifications.The objective of MANET ...Mobile Ad Hoc Network(MANET)is a group of node that would interrelate among each other through onemulti-hop wireless link,wherein the nodes were able to move in response to sudden modifications.The objective of MANET routing protocol is to quantify the route and compute the best path,but there exists a major decrease in energy efficiency,difficulty in hop selection,cost estimation,and efficient load-balancing.In this paper,a novel least common multipath-based routing has been proposed.Multipath routing is used to find a multipath route from source and destination.Load balancing is of primary importance in the mobile ad-hoc networks,due to limited bandwidth among the nodes and the initiator of the load routing discovery phase in the multipath routing protocol.Fuzzy logic for load balancing multipath routing in MANETs is proposed,which ensures the data packets are sent through a path with the variance of binary sets to predict the original transformation of the data to be received in the system.The main objective of the proposed system is to reduce the routing time of data packets and avoid the traffic based on multipath source and destination.The experimental results have to verify 96.7%efficiency in balancing the load.展开更多
A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H...A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.展开更多
Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define t...Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define the arithmetic function G_(k,f)(n)to be∏_(i=0)^(k)|f(n+i)|/lcm0≤i≤k{f(n+i)}for all n∈N^(+)\Z_(k,f),where N^(+) is the set of positive integers and Z_(k,f):=∪_(j=0)^(k){n∈N^(+):f(n+j)=0}.When the degree of f(x)is 1 or 2,the periodicity of G_(k,f) were studied well by Hong and Qian.In 2020,Lin and Hong investigated the periodicity of G_(k,f) when f(x)=x^(3)+2.In this paper,we study the periodicity of G_(k,f) with f(x)=x^(3)+4.We show that G_(k,f) is a periodic arithmetic function and then determine the smallest period of G_(k,f).Furthermore,an asymptotic formula for loglcm0≤i≤k{(n+i)^(3)+4}is given as n goes to infinity.The proof of our result uses analytic and p-adic methods.展开更多
This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and gene...This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.展开更多
Drought stress linked with climate change is one of the major constraints faced by common bean farmers in Africa and elsewhere. Mitigating this constraint requires the selection of resilient varieties that withstand d...Drought stress linked with climate change is one of the major constraints faced by common bean farmers in Africa and elsewhere. Mitigating this constraint requires the selection of resilient varieties that withstand drought threats to common bean production.This study assessed the drought response of 64 small red-seeded genotypes of common bean grown in a lattice design replicated twice under contrasting moisture regimes,terminal drought stress and non-stress, in Ethiopia during the dry season from November2014 to March 2015. Multiple plant traits associated with drought were assessed for their contribution to drought adaptation of the genotypes. Drought stress determined by a drought intensity index was moderate(0.3). All the assessed traits showed significantly different genotypic responses under drought stress and non-stress conditions. Eleven genotypes significantly(P ≤ 0.05) outperformed the drought check cultivar under both drought stress and non-stress conditions in seed yielding potential. Seed yield showed positive and significant correlations with chlorophyll meter reading, vertical root pulling resistance force, number of pods per plant, and seeds per pod under both soil moisture regimes, indicating their potential use in selection of genotypes yielding well under drought stress and non-stress conditions. Clustering analysis using Mahalanobis distance grouped the genotypes into four groups showing high and significant inter-cluster distance, suggesting that hybridization between drought-adapted parents from the groups will provide the maximum genetic recombination for drought tolerance in subsequent generations.展开更多
基金The undergraduate teaching reform project of Nanning Normal University in 2023“Construction and Practice of Curriculum Teaching Community of the Course‘Introduction to Tourism Management’from the Perspective of Multiple Collaborative”(2023JGX037)。
文摘Through the empirical research on the teaching of undergraduate professional introduction courses,the teaching experience of similar high-quality courses is refined.Based on modern educational technology,the innovative thinking of similar course teaching is explored.By establishing a teaching community to facilitate multi-dimensional collaboration,this approach overcomes the constraints of time and space,effectively integrates teaching resources,and enhances the scientific rigor,standardization,and effectiveness of course instruction.As a result,the educational impact of professional introduction courses is continuously optimized.
基金Supported by the General Project of Science and Technology Department of Sichuan Province(2018JY0256)the Scientific Research Fund of Leshan Normal University(DGZZ202024)。
文摘The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.
文摘Mobile Ad Hoc Network(MANET)is a group of node that would interrelate among each other through onemulti-hop wireless link,wherein the nodes were able to move in response to sudden modifications.The objective of MANET routing protocol is to quantify the route and compute the best path,but there exists a major decrease in energy efficiency,difficulty in hop selection,cost estimation,and efficient load-balancing.In this paper,a novel least common multipath-based routing has been proposed.Multipath routing is used to find a multipath route from source and destination.Load balancing is of primary importance in the mobile ad-hoc networks,due to limited bandwidth among the nodes and the initiator of the load routing discovery phase in the multipath routing protocol.Fuzzy logic for load balancing multipath routing in MANETs is proposed,which ensures the data packets are sent through a path with the variance of binary sets to predict the original transformation of the data to be received in the system.The main objective of the proposed system is to reduce the routing time of data packets and avoid the traffic based on multipath source and destination.The experimental results have to verify 96.7%efficiency in balancing the load.
文摘A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.
文摘Let k be an arbitrary positive integer and f(x)a polynomial with integer coefficients.Associated to the least common multiple lcm0≤i≤k{f(n+i)}of any k+1 consecutive terms in the sequence{f(n)}_(n=1)^(∞),we define the arithmetic function G_(k,f)(n)to be∏_(i=0)^(k)|f(n+i)|/lcm0≤i≤k{f(n+i)}for all n∈N^(+)\Z_(k,f),where N^(+) is the set of positive integers and Z_(k,f):=∪_(j=0)^(k){n∈N^(+):f(n+j)=0}.When the degree of f(x)is 1 or 2,the periodicity of G_(k,f) were studied well by Hong and Qian.In 2020,Lin and Hong investigated the periodicity of G_(k,f) when f(x)=x^(3)+2.In this paper,we study the periodicity of G_(k,f) with f(x)=x^(3)+4.We show that G_(k,f) is a periodic arithmetic function and then determine the smallest period of G_(k,f).Furthermore,an asymptotic formula for loglcm0≤i≤k{(n+i)^(3)+4}is given as n goes to infinity.The proof of our result uses analytic and p-adic methods.
文摘This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.
基金funding to D. Ambachew, A. Asfaw, and M. W. Blair by the Tropical Legumes project of the Generation Challenge Program (C-086-13) with support from the Bill and Melinda Gates FoundationThe Evans Allen Fund is recognized for funding Matthew W. Blair and Daniel Ambachew at Tennessee State University
文摘Drought stress linked with climate change is one of the major constraints faced by common bean farmers in Africa and elsewhere. Mitigating this constraint requires the selection of resilient varieties that withstand drought threats to common bean production.This study assessed the drought response of 64 small red-seeded genotypes of common bean grown in a lattice design replicated twice under contrasting moisture regimes,terminal drought stress and non-stress, in Ethiopia during the dry season from November2014 to March 2015. Multiple plant traits associated with drought were assessed for their contribution to drought adaptation of the genotypes. Drought stress determined by a drought intensity index was moderate(0.3). All the assessed traits showed significantly different genotypic responses under drought stress and non-stress conditions. Eleven genotypes significantly(P ≤ 0.05) outperformed the drought check cultivar under both drought stress and non-stress conditions in seed yielding potential. Seed yield showed positive and significant correlations with chlorophyll meter reading, vertical root pulling resistance force, number of pods per plant, and seeds per pod under both soil moisture regimes, indicating their potential use in selection of genotypes yielding well under drought stress and non-stress conditions. Clustering analysis using Mahalanobis distance grouped the genotypes into four groups showing high and significant inter-cluster distance, suggesting that hybridization between drought-adapted parents from the groups will provide the maximum genetic recombination for drought tolerance in subsequent generations.
