The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e...The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.展开更多
In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b...In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.展开更多
We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using the...We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.展开更多
Phosphorus（P） is an important macronutrient for plant but can also cause potential environmental risk. In this paper, we studied the long-term fertilizer experiment（started 1980） to assess the soil P dynamic, bala...Phosphorus（P） is an important macronutrient for plant but can also cause potential environmental risk. In this paper, we studied the long-term fertilizer experiment（started 1980） to assess the soil P dynamic, balance, critical P value and the crop yield response in Taihu Lake region, China. To avoid the effect of nitrogen（N） and potassium（K）, only the following treatments were chosen for subsequent discussion, including： C0（control treatment without any fertilizer or organic manure）, CNK treatment（mineral N and K only）, CNPK（balanced fertilization with mineral N, P and K）, MNK（integrated organic manure and mineral N and K）, and MNPK（organic manure plus balanced fertilization）. The results revealed that the response of wheat yield was more sensitive than rice, and no significant differences of crop yield had been detected among MNK, CNPK and MNPK until 2013. Dynamic and balance of soil total P（TP） and Olsen-P showed soil TP pool was enlarged significantly over consistent fertilization. However, the diminishing marginal utility of soil Olsen-P was also found, indicating that high-level P application in the present condition could not increase soil Olsen-P contents anymore. Linear-linear and Mitscherlich models were used to estimate the critical value of Olsen-P for crops. The average critical P value for rice and wheat was 3.40 and 4.08 mg kg^（–1）, respectively. The smaller critical P value than in uplands indicated a stronger ability of P supply for crops in this paddy soil. We concluded that no more mineral P should be applied in rice-wheat system in Taihu Lake region if soil Olsen-P is higher than the critical P value. The agricultural technique and management referring to activate the plant-available P pool are also considerable, such as integrated use of low-P organic manure with mineral N and K.展开更多
In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach sp...In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.展开更多
Adding a reputation incentive system to peer-to-peer(P2P)energy transactions can encourage prosumers to regulate their trading behavior,which is important for ensuring the efficiency and reliability of P2P transaction...Adding a reputation incentive system to peer-to-peer(P2P)energy transactions can encourage prosumers to regulate their trading behavior,which is important for ensuring the efficiency and reliability of P2P transactions.This study proposed a P2P transaction mechanism and game optimization model for prosumers involved in distributed energy sources considering reputation-value incentives.First,the deviation of P2P transactions and the non-consumption rate of distributed renewable energy in P2P transactions were established as indicators to quantify the influencing factors of the reputation value,and a reputation incentive model of P2P transactions for prosumers was constructed.Then,the penalty coefficient was applied to the cost function of the prosumers,and a non-cooperative game model of P2P transactions based on the complete information of multi-prosumers was established.Furthermore,the Nash equilibrium problem was transformed into a nonlinear optimization problem by constructing the modified optimal reaction function,and the Nash equilibrium solution of the game was obtained via a relaxation algorithm.Finally,the modified IEEE 33-node test system based on electricity market P2P and an IEEE 123-node test system were used to analyze and verify the cost and P2P participation of prosumers considering the reputation value.The results show that the addition of the reputation incentive system can encourage prosumers to standardize their interactive transaction behavior and actively participate in P2P transactions.It can also improve the operation efficiency of the power grid and promote the perfection of the P2P transaction mechanism.展开更多
In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the ...In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.展开更多
The problem of price scissors difference between industrial products and agricultural products is one of the important problems in China. It impacts not only the living standard improvement of farmers but also the eco...The problem of price scissors difference between industrial products and agricultural products is one of the important problems in China. It impacts not only the living standard improvement of farmers but also the economic value of cultivated land, furthermore results in the direct and indirect loss of cultivated land resources. China＇s cultivated land area has decreased dramatically in recent years. An important reason for the decrease is the relatively low cost of cultivated land occupancy, which results from the distortion of economic value of cultivated land due to the existence of scissors difference. This study firstly analyzed the dynamic change of scissors difference and calculated the absolute and relative magnitude of scissors difference from 1997 to 2002, then computed the economic value of cultivated land before and after scissors difference adjustment in 2002, and finally discussed the inverted scissors difference. Results suggest that the scissors difference has a remarkable impact on the economic value of cultivated land, and the adjustment of scissors difference even inverted scissors difference to the economic value of cultivated land is indisoensable.展开更多
In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong mar...In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong martingales.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ...Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.展开更多
In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φp（u000））0（t）＋a（t）f（t, u（t？τ）, u0（t））=0, 0〈t〈1;u000 （0）=u00 （0）=0,...In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φp（u000））0（t）＋a（t）f（t, u（t？τ）, u0（t））=0, 0〈t〈1;u000 （0）=u00 （0）=0, u0 （1）=αu0 （η）;u（t）=0, ？τ ≤t≤0. By using Schauder fixed-point theorem, some su？cient conditions are obtained which guar-antee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.展开更多
Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very ...Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very useful for grayscale secret images.In this method,the secret image decomposes in three parts based on the pixel’s threshold value.The division of the color image into three parts is very easy based on the color channel but in the grayscale image,it is difficult to implement.The proposed image scrambling method is implemented in image steganography using discrete wavelet transform(DWT),singular value decomposition(SVD),and sorting function.There is no visual difference between the stego image and the cover image.The extracted secret image is also similar to the original secret image.The proposed algorithm outcome is compared with the existed image steganography techniques.The comparative results show the strength of the proposed technique.展开更多
AIM： To propose a new meta-analysis method for bi-variate P value which account for the paired structure. METHODS： Studies that look to test two different fea-tures from the same sample gives rise to bivariate Pvalu...AIM： To propose a new meta-analysis method for bi-variate P value which account for the paired structure. METHODS： Studies that look to test two different fea-tures from the same sample gives rise to bivariate Pvalue. A relevant example of this is testing for periodici-ty as well expression from time-course gene expressionstudies. Kocak et al （2010） uses George and Mudholkar’（1983） “Difference of Two Logit-Sums” method to poolbivariate P value across independent experiments, as-suming independence within a pair. As bivariate P valueneed not to be independent within a given study, wepropose a new meta-analysis approach for pooling bi-variate P value across independent experiments, whichaccounts for potential correlation between paired P-val-ues. We compare the “Difference of Two Logit Sums”method with our novel approach in terms of their sen-sitivity and specifcity through extensive simulations by generating P value samples from most commonly used tests namely, Z test, t test, chi-square test, and F test, with varying sample sizes and correlation structure. RESULTS： The simulations results showed that our new meta-analysis approach for correlated and uncor-related bivariate P value has much more desirable sen-sitivity and specifcity features compared to the existing method, which treats each member of the paired P value as independent. We also compare these meta-analysis approaches on bivariate P value from periodici-ty and expression tests of 4936 S.Pombe genes from 10 independent time-course experiments and we showed that our new approach ranks the periodic, conserved, and cycling genes significantly higher, and detects many more periodic, “conserved” and “cycling” genes among the top 100 genes, compared to the ‘Difference of Two Logit-Sums’ method. Finally, we used our meta-analytic approach to compare the relative evidence in the association of pre-term birth with preschool wheez-ing versus pre-school asthma.CONCLUSION： The new meta-analysis method has much better sensitivity and specifc characteristics com-pared to the “Difference of Two-Logit Sums” method and it is not computationally more expensive.展开更多
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
文摘The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.
文摘In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.
文摘We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.
基金supported by the Special Fund for Agro-scientific Research in the Public Interest of China(201203030)the Science and Technology Support Program of Jiangsu,China(BE2013334)the Agricultural Science&Technology Innovation Foundation of Jiangsu Province,China(CX(14)5085)
文摘Phosphorus（P） is an important macronutrient for plant but can also cause potential environmental risk. In this paper, we studied the long-term fertilizer experiment（started 1980） to assess the soil P dynamic, balance, critical P value and the crop yield response in Taihu Lake region, China. To avoid the effect of nitrogen（N） and potassium（K）, only the following treatments were chosen for subsequent discussion, including： C0（control treatment without any fertilizer or organic manure）, CNK treatment（mineral N and K only）, CNPK（balanced fertilization with mineral N, P and K）, MNK（integrated organic manure and mineral N and K）, and MNPK（organic manure plus balanced fertilization）. The results revealed that the response of wheat yield was more sensitive than rice, and no significant differences of crop yield had been detected among MNK, CNPK and MNPK until 2013. Dynamic and balance of soil total P（TP） and Olsen-P showed soil TP pool was enlarged significantly over consistent fertilization. However, the diminishing marginal utility of soil Olsen-P was also found, indicating that high-level P application in the present condition could not increase soil Olsen-P contents anymore. Linear-linear and Mitscherlich models were used to estimate the critical value of Olsen-P for crops. The average critical P value for rice and wheat was 3.40 and 4.08 mg kg^（–1）, respectively. The smaller critical P value than in uplands indicated a stronger ability of P supply for crops in this paddy soil. We concluded that no more mineral P should be applied in rice-wheat system in Taihu Lake region if soil Olsen-P is higher than the critical P value. The agricultural technique and management referring to activate the plant-available P pool are also considerable, such as integrated use of low-P organic manure with mineral N and K.
基金Supported by the National Natural Science Foundation of China
文摘In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.
基金supported by the National Natural Science Foundation of China(U2066211,52177124,52107134)the Institute of Electrical Engineering,CAS(E155610101)+1 种基金the DNL Cooperation Fund,CAS(DNL202023)the Youth Innovation Promotion Association of CAS(2019143).
文摘Adding a reputation incentive system to peer-to-peer(P2P)energy transactions can encourage prosumers to regulate their trading behavior,which is important for ensuring the efficiency and reliability of P2P transactions.This study proposed a P2P transaction mechanism and game optimization model for prosumers involved in distributed energy sources considering reputation-value incentives.First,the deviation of P2P transactions and the non-consumption rate of distributed renewable energy in P2P transactions were established as indicators to quantify the influencing factors of the reputation value,and a reputation incentive model of P2P transactions for prosumers was constructed.Then,the penalty coefficient was applied to the cost function of the prosumers,and a non-cooperative game model of P2P transactions based on the complete information of multi-prosumers was established.Furthermore,the Nash equilibrium problem was transformed into a nonlinear optimization problem by constructing the modified optimal reaction function,and the Nash equilibrium solution of the game was obtained via a relaxation algorithm.Finally,the modified IEEE 33-node test system based on electricity market P2P and an IEEE 123-node test system were used to analyze and verify the cost and P2P participation of prosumers considering the reputation value.The results show that the addition of the reputation incentive system can encourage prosumers to standardize their interactive transaction behavior and actively participate in P2P transactions.It can also improve the operation efficiency of the power grid and promote the perfection of the P2P transaction mechanism.
基金Supported by the Key Discipline Construction Project of Tianshui Normal University
文摘In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.
文摘The problem of price scissors difference between industrial products and agricultural products is one of the important problems in China. It impacts not only the living standard improvement of farmers but also the economic value of cultivated land, furthermore results in the direct and indirect loss of cultivated land resources. China＇s cultivated land area has decreased dramatically in recent years. An important reason for the decrease is the relatively low cost of cultivated land occupancy, which results from the distortion of economic value of cultivated land due to the existence of scissors difference. This study firstly analyzed the dynamic change of scissors difference and calculated the absolute and relative magnitude of scissors difference from 1997 to 2002, then computed the economic value of cultivated land before and after scissors difference adjustment in 2002, and finally discussed the inverted scissors difference. Results suggest that the scissors difference has a remarkable impact on the economic value of cultivated land, and the adjustment of scissors difference even inverted scissors difference to the economic value of cultivated land is indisoensable.
文摘In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong martingales.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
基金Supported by the Natural Science Foundation of Hunan Province（06JJ50008） Supported by the Natural Science Foundation of Guangdong Province（7004569）
文摘Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.
基金Foundation item： Supported by the National Natural Science Foundation of China（10801001） Supported by the Natural Science Foundation of Anhui Province（1208085MA13, KJ2009A005Z）
文摘In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φp（u000））0（t）＋a（t）f（t, u（t？τ）, u0（t））=0, 0〈t〈1;u000 （0）=u00 （0）=0, u0 （1）=αu0 （η）;u（t）=0, ？τ ≤t≤0. By using Schauder fixed-point theorem, some su？cient conditions are obtained which guar-antee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.
基金This work was supported by Taif university Researchers Supporting Project Number(TURSP-2020/114),Taif University,Taif,Saudi Arabia.
文摘Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very useful for grayscale secret images.In this method,the secret image decomposes in three parts based on the pixel’s threshold value.The division of the color image into three parts is very easy based on the color channel but in the grayscale image,it is difficult to implement.The proposed image scrambling method is implemented in image steganography using discrete wavelet transform(DWT),singular value decomposition(SVD),and sorting function.There is no visual difference between the stego image and the cover image.The extracted secret image is also similar to the original secret image.The proposed algorithm outcome is compared with the existed image steganography techniques.The comparative results show the strength of the proposed technique.
文摘AIM： To propose a new meta-analysis method for bi-variate P value which account for the paired structure. METHODS： Studies that look to test two different fea-tures from the same sample gives rise to bivariate Pvalue. A relevant example of this is testing for periodici-ty as well expression from time-course gene expressionstudies. Kocak et al （2010） uses George and Mudholkar’（1983） “Difference of Two Logit-Sums” method to poolbivariate P value across independent experiments, as-suming independence within a pair. As bivariate P valueneed not to be independent within a given study, wepropose a new meta-analysis approach for pooling bi-variate P value across independent experiments, whichaccounts for potential correlation between paired P-val-ues. We compare the “Difference of Two Logit Sums”method with our novel approach in terms of their sen-sitivity and specifcity through extensive simulations by generating P value samples from most commonly used tests namely, Z test, t test, chi-square test, and F test, with varying sample sizes and correlation structure. RESULTS： The simulations results showed that our new meta-analysis approach for correlated and uncor-related bivariate P value has much more desirable sen-sitivity and specifcity features compared to the existing method, which treats each member of the paired P value as independent. We also compare these meta-analysis approaches on bivariate P value from periodici-ty and expression tests of 4936 S.Pombe genes from 10 independent time-course experiments and we showed that our new approach ranks the periodic, conserved, and cycling genes significantly higher, and detects many more periodic, “conserved” and “cycling” genes among the top 100 genes, compared to the ‘Difference of Two Logit-Sums’ method. Finally, we used our meta-analytic approach to compare the relative evidence in the association of pre-term birth with preschool wheez-ing versus pre-school asthma.CONCLUSION： The new meta-analysis method has much better sensitivity and specifc characteristics com-pared to the “Difference of Two-Logit Sums” method and it is not computationally more expensive.
