J. Appl. Math.最新文献

{"title":"2D Sin-Cos-Henon Map for Color Image Encryption with High Security","authors":"Zhiqiang Cheng, Wencheng Wang, Yuezhang Dai, Lun Li","doi":"10.1155/2022/9508749","DOIUrl":"https://doi.org/10.1155/2022/9508749","url":null,"abstract":"In this paper, a high security color image encryption algorithm is proposed by 2D Sin-Cos-Hénon (2D-SCH) system. A new two-dimensional chaotic system which is 2D-SCH. This system is hyperchaotic. The use of the 2D-SCH, a color image encryption algorithm based on random scrambling and localization diffusion, is proposed. First, the secret key is generated by SHA512 through plaintext. As the initial value of the 2D-SCH system, the secret key is used to generate chaotic sequences. Then, the random scrambling is designed based on chaotic sequences. Finally, a pair of initial points is generated by the secret key; the image diffuses around this point. The ciphertext is obtained by a double encryption. Different from the traditional encryption algorithm, this paper encrypts three channels of color image simultaneously, which greatly improves the security of the algorithm. Simulation results show that the algorithm can resist various attacks.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"435 1","pages":"9508749:1-9508749:11"},"PeriodicalIF":0.0,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86850827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability","authors":"N. Mahmudov","doi":"10.1155/2022/2661343","DOIUrl":"https://doi.org/10.1155/2022/2661343","url":null,"abstract":"<jats:p>We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 <mo>,</mo>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mi>z</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>+</mo>\u0000 <mi>A</mi>\u0000 <mi>z</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>+</mo>\u0000 <mi>Ω</mi>\u0000 <mi>z</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>−</mo>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> of order <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mn>1</mn>\u0000 <mo><</mo>\u0000 <mi>μ</mi>\u0000 <mo><</mo>\u0000 <mn>2</mn>\u0000 </math>\u0000 </jats:inline-formula> and type <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mn>0</mn>\u0000 <mo>≤</mo>\u0000 <mi>ν</mi>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </math>\u0000 </jats:inline-formula>, with nonpermutable matrices <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"2014 1","pages":"2661343:1-2661343:7"},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73315462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Benefits of Fluctuating Exchange Rates on the Investor's Wealth","authors":"Obonye Doctor, E. Lungu","doi":"10.1155/2022/5595610","DOIUrl":"https://doi.org/10.1155/2022/5595610","url":null,"abstract":"<jats:p>We consider a problem of maximizing the utility of an agent who invests in a stock and a money market account incorporating proportional transaction costs <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> and foreign exchange rate fluctuations. Assuming a HARA utility function <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>U</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mi>p</mi>\u0000 </math>\u0000 </jats:inline-formula> for all <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>c</mi>\u0000 <mo>≥</mo>\u0000 <mn>0</mn>\u0000 </math>\u0000 </jats:inline-formula>, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mn>1</mn>\u0000 </math>\u0000 </jats:inline-formula>, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>p</mi>\u0000 <mo>≠</mo>\u0000 <mn>0</mn>\u0000 </math>\u0000 </jats:inline-formula>, we suggest an approach of determining the value function. Contrary to fears associated with exchange rate fluctuations, our results show that these fluctuations can bring about tangible benefits in one’s wealth. We quantify the level of these benefits. We also present an example which illustrates an investment strategy of our agent.</jats:p>","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"11 1","pages":"5595610:1-5595610:10"},"PeriodicalIF":0.0,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83368662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation Analysis of a 5D Nutrient, Plankton, Limnothrissa miodon Model with Hydrocynus vittatus Predation","authors":"F. K. Mutasa, Brian Jones, I. Tendaupenyu, T. Nhiwatiwa, Mzime R. Ndebele-Murisa","doi":"10.1155/2022/1095441","DOIUrl":"https://doi.org/10.1155/2022/1095441","url":null,"abstract":"In this paper, we construct and analyze a theoretical, deterministic \u0000 \u0000 5\u0000 \u0000 D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"219 1","pages":"1095441:1-1095441:21"},"PeriodicalIF":0.0,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78597470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A High-Security Privacy Image Encryption Algorithm Based on Chaos and Double Encryption Strategy","authors":"Zhiqiang Cheng, Wencheng Wang, Yuezhang Dai, Lun Li","doi":"10.1155/2022/9040702","DOIUrl":"https://doi.org/10.1155/2022/9040702","url":null,"abstract":"Faces are widely used in information recognition and other fields. Due to the openness of the Internet, ensuring that face information is not stolen by criminals is a hot issue. The traditional encryption method only encrypts the whole area of the image and ignores some features of the face. This paper proposes a double-encrypted face image encryption algorithm. The contour features of the face are extracted, followed by two rounds of encryption. The first round of encryption algorithm encrypts the identified face image, and the second round of encryption algorithm encrypts the entire image. The encryption algorithm used is scrambling and diffusion at the same time, and the keystream of the cryptosystem is generated by 2D SF-SIMM. The design structure of this cryptosystem increases security, and the attacker needs to crack two rounds of the algorithm to get the original face image.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"19 1","pages":"9040702:1-9040702:14"},"PeriodicalIF":0.0,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80354249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modified Oscillation Results for Advanced Difference Equations of Second-Order","authors":"G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani","doi":"10.1155/2022/3407776","DOIUrl":"https://doi.org/10.1155/2022/3407776","url":null,"abstract":"<jats:p>In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>Δ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>η</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mi>Δ</mi>\u0000 <mi>υ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>+</mo>\u0000 <mi>ρ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mi>υ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 </math>\u0000 </jats:inline-formula> using the ordinary difference equation <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>Δ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>η</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mi>Δ</mi>\u0000 <mi>υ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>+</mo>\u0000 <mi>q</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 ","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"11 1","pages":"3407776:1-3407776:5"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83527152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation","authors":"Jin Li","doi":"10.1155/2022/8998193","DOIUrl":"https://doi.org/10.1155/2022/8998193","url":null,"abstract":"Nonlinear heat equation solved by the barycentric rational collocation method (BRCM) is presented. Direct linearization method and Newton linearization method are presented to transform the nonlinear heat conduction equation into linear equations. The matrix form of nonlinear heat conduction equation is also obtained. Several numerical examples are provided to valid our schemes.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"21 1","pages":"8998193:1-8998193:9"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72918402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential","authors":"M. J. Idrisi, Teklehaimanot Eshetie, Tenaw Tilahun, Mitiku Kerebh","doi":"10.1155/2022/4072418","DOIUrl":"https://doi.org/10.1155/2022/4072418","url":null,"abstract":"<jats:p>We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>α</mi>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>λ</mi>\u0000 </math>\u0000 </jats:inline-formula> on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>α</mi>\u0000 <mo>∈</mo>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> is the coupling constant of Yukawa force to gravitational force, and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>λ</mi>\u0000 <mo>∈</mo>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mrow>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>∞</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> is the range of Yukawa force. It is observed that as <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>λ</mi>\u0000 <mo>⟶</mo>\u0000 <mo>∞</mo>\u0000 </math>\u0000 </jats:inline-formula>, the mean-motion of the primaries <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>n</mi>\u0000 <mo>⟶</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>+</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 ","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"44 1","pages":"4072418:1-4072418:6"},"PeriodicalIF":0.0,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82482119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hydrodynamic Boundary Layer Flow of Chemically Reactive Fluid over Exponentially Stretching Vertical Surface with Transverse Magnetic Field in Unsteady Porous Medium","authors":"M. Sulemana, I. Y. Seini, O. Makinde","doi":"10.1155/2022/7568695","DOIUrl":"https://doi.org/10.1155/2022/7568695","url":null,"abstract":"This article addresses the hydrodynamic boundary layer flow of a chemically reactive fluid over an exponentially stretching vertical surface with transverse magnetic field in an unsteady porous medium. The flow problem is modelled as time depended dimensional partial differential equations which are transformed to dimensionless equations and solved by means of approximate analytic method. The results are illustrated graphically and numerically and compared with previously published results which shown a good agreement. Physically increasing Eckert number of a fluid amplifies the kinetic energy of the fluid, and as a novelty, the Eckert number under the influence of chemically reactive magnetic field is effective in controlling the kinematics of hydrodynamic boundary layer flow in porous medium. Interestingly, whilst the Eckert number amplifies the thermal boundary layer thickness and velocity as well as the concentration of the fluid, the presence of the magnetic field and the strength of the chemical reaction have a retarding effect on the flow. Also, the chemical reaction parameter and permeability of porous medium are effective in reducing skin friction in chemically reactive magnetic porous medium and are relevant in practice because reduced skin friction enhances the efficiency of a system. The results of the current study are useful in solar energy collector systems and materials processing.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"24 1","pages":"7568695:1-7568695:11"},"PeriodicalIF":0.0,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73940617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model","authors":"A. El koufi, N. El Koufi, A. Bennar, N. S. Rao","doi":"10.1155/2022/4796273","DOIUrl":"https://doi.org/10.1155/2022/4796273","url":null,"abstract":"At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value \u0000 \u0000 \u0000 \u0000 Π\u0000 \u0000 \u0000 s\u0000 \u0000 \u0000 \u0000 of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"219 1","pages":"4796273:1-4796273:11"},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79789744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}