Edoardo Persichetti, T. Randrianarisoa, P. Santini
Abstract A recent paper by Zhang and Zhang claims to construct the first code-based non-interactive key exchange protocol, using a modified version of the Code Equivalence Problem. In this paper we explain why this approach is flawed. Namely, we describe an attack which involves only linear algebra and completely breaks the protocol with overwhelming probability. A simple Magma script confirms our results.
{"title":"An Attack on a Non-Interactive Key Exchange from Code Equivalence","authors":"Edoardo Persichetti, T. Randrianarisoa, P. Santini","doi":"10.2478/tmmp-2022-0018","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0018","url":null,"abstract":"Abstract A recent paper by Zhang and Zhang claims to construct the first code-based non-interactive key exchange protocol, using a modified version of the Code Equivalence Problem. In this paper we explain why this approach is flawed. Namely, we describe an attack which involves only linear algebra and completely breaks the protocol with overwhelming probability. A simple Magma script confirms our results.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"82 1","pages":"53 - 64"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42018355","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}
Abstract This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of q-ary expansions.
摘要本文致力于用广义移位算子定义有理数可由q-元展开的某些正推广表示的条件。
{"title":"The Generalized Shifts and Rational Numbers","authors":"S. Serbenyuk","doi":"10.2478/tmmp-2022-0015","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0015","url":null,"abstract":"Abstract This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of q-ary expansions.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"82 1","pages":"9 - 16"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44034379","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}
Abstract We derive recurrence relations for the squares of the Horadam numbers wn2 w_n^2 , where the Horadam sequence wn is such that the numbers wn, for n ∈ ℤ, are defined recursively by w0 = a, w1 = b, wn = pwn−1 − qwn−2 (n ≥ 2), where a, b, p and q are arbitrary complex numbers with p ≠ 0 and q ≠ 0. Some related results emanating from the recurrence relations such as reciprocal sums, partial sums, and sums with double binomial coefficients are also presented.
{"title":"Recurrence Relations for the Squares of the Horadam Numbers and Some Associated Consequences","authors":"K. Adegoke, R. Frontczak, T. Goy","doi":"10.2478/tmmp-2022-0016","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0016","url":null,"abstract":"Abstract We derive recurrence relations for the squares of the Horadam numbers wn2 w_n^2 , where the Horadam sequence wn is such that the numbers wn, for n ∈ ℤ, are defined recursively by w0 = a, w1 = b, wn = pwn−1 − qwn−2 (n ≥ 2), where a, b, p and q are arbitrary complex numbers with p ≠ 0 and q ≠ 0. Some related results emanating from the recurrence relations such as reciprocal sums, partial sums, and sums with double binomial coefficients are also presented.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"82 1","pages":"17 - 28"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49406230","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}
Abstract This paper deals with historical encrypted manuscripts and introduces an automated method for the detection and transcription of ciphertext symbols for subsequent cryptanalysis. Our database contains documents used in the past by aristocratic families living in the territory of Slovakia. They are encrypted using a nomenclator which is a specific type of substitution cipher. In our case, the nomenclator uses digits as ciphertext symbols. We have proposed a method for the detection, classification, and transcription of handwritten digits from the original documents. Our method is based on Mask R-CNN which is a deep convolutional neural network for instance segmentation. Mask R-CNN was trained on a manually collected database of digit annotations. We employ a specific strategy where the input image is first divided into small blocks. The image blocks are then passed to Mask R-CNN to obtain detections. This way we avoid problems related to the detection of a large number of small dense objects in a high-resolution image. Experiments have shown promising detection performance for all digit types with minimum false detections.
{"title":"Automated Transcription of Historical Encrypted Manuscripts","authors":"Eugen Antal, Pavol Marák","doi":"10.2478/tmmp-2022-0019","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0019","url":null,"abstract":"Abstract This paper deals with historical encrypted manuscripts and introduces an automated method for the detection and transcription of ciphertext symbols for subsequent cryptanalysis. Our database contains documents used in the past by aristocratic families living in the territory of Slovakia. They are encrypted using a nomenclator which is a specific type of substitution cipher. In our case, the nomenclator uses digits as ciphertext symbols. We have proposed a method for the detection, classification, and transcription of handwritten digits from the original documents. Our method is based on Mask R-CNN which is a deep convolutional neural network for instance segmentation. Mask R-CNN was trained on a manually collected database of digit annotations. We employ a specific strategy where the input image is first divided into small blocks. The image blocks are then passed to Mask R-CNN to obtain detections. This way we avoid problems related to the detection of a large number of small dense objects in a high-resolution image. Experiments have shown promising detection performance for all digit types with minimum false detections.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"82 1","pages":"65 - 86"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42535593","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}
Abstract The aim of this paper is to study sequences of numbers as random variables. The asymptotic density will play the role of the probability. In the first part of this paper, the notion of natural metric on the set of natural numbers is defined. It is a metric so that the completion of ℕ is a compact metric space on which a probability Borel measure exists so that the sequence {n} is uniformly distributed. This condition connects the asymptotic density and the mentioned measure. A necessary and sufficient condition is derived so that a given metric is natural. Later, we study the properties of sequences uniformly continuous with respect to the given natural metric. Inter alia, the continuity ofdistribution function is characterized.
{"title":"Metrics on ℕ and the Distribution of Sequences","authors":"M. Paštéka","doi":"10.2478/tmmp-2022-0017","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0017","url":null,"abstract":"Abstract The aim of this paper is to study sequences of numbers as random variables. The asymptotic density will play the role of the probability. In the first part of this paper, the notion of natural metric on the set of natural numbers is defined. It is a metric so that the completion of ℕ is a compact metric space on which a probability Borel measure exists so that the sequence {n} is uniformly distributed. This condition connects the asymptotic density and the mentioned measure. A necessary and sufficient condition is derived so that a given metric is natural. Later, we study the properties of sequences uniformly continuous with respect to the given natural metric. Inter alia, the continuity ofdistribution function is characterized.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"82 1","pages":"29 - 52"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47866419","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}
Pub Date : 2022-11-28DOI: 10.48550/arXiv.2211.15184
G. Lupi, K. Mikula, Seol Ah Park
Abstract When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these trajectories, we present a mathematical model and numerical method based on evolving open-plane curve approach in the Lagrangian formulation. The model contains two terms: the first is the smoothing term given by the influence of local curvature, while the other attracts the curve to the original trajectory. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. The PDE includes the asymptotically uniform tangential redistribution of curve grid points. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve.
{"title":"Macrophages Trajectories Smoothing by Evolving Curves","authors":"G. Lupi, K. Mikula, Seol Ah Park","doi":"10.48550/arXiv.2211.15184","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15184","url":null,"abstract":"Abstract When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these trajectories, we present a mathematical model and numerical method based on evolving open-plane curve approach in the Lagrangian formulation. The model contains two terms: the first is the smoothing term given by the influence of local curvature, while the other attracts the curve to the original trajectory. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. The PDE includes the asymptotically uniform tangential redistribution of curve grid points. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79584949","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}
Abstract It is proved that for an extremally disconnected S-paracompact-T2 spaces the properties semi-Menger, Menger, strongly star semi-Menger, strongly star-Menger, star semi-Menger, star-Menger, almost semi-Menger, almost Menger, almost star semi-Menger, almost star-Menger are equivalent. We show that a weakly semi-continuous (strongly θ-semi-continuous) image of semi-Menger (almost semi-Menger) spaces is almost semi-Menger (semi-Menger), respectively. The characterizations of semi-Menger and star semi-Menger spaces are also provided.
{"title":"Remarks on Semi-Menger and Star Semi-Menger Spaces","authors":"G. Kumar, B. K.Tyagi","doi":"10.2478/tmmp-2022-0003","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0003","url":null,"abstract":"Abstract It is proved that for an extremally disconnected S-paracompact-T2 spaces the properties semi-Menger, Menger, strongly star semi-Menger, strongly star-Menger, star semi-Menger, star-Menger, almost semi-Menger, almost Menger, almost star semi-Menger, almost star-Menger are equivalent. We show that a weakly semi-continuous (strongly θ-semi-continuous) image of semi-Menger (almost semi-Menger) spaces is almost semi-Menger (semi-Menger), respectively. The characterizations of semi-Menger and star semi-Menger spaces are also provided.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"81 1","pages":"57 - 68"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42862092","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}
Abstract In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δnm), where ℋ represents one of the spaces ℓ∞, c or c0.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {c, c0} will be given. Also, some matrix characterizations concerning these spaces will be computed. Moreover, the characterization of some classes of compact operators on the spaces ℓ∞(f, g, Δnm)and c0(f, g, Δnm)by employing the Hausdorff measure of non-compactness will be determined.
{"title":"On Some Properties of Difference Operator with Some Characterizations","authors":"D. Fathima, A. Ganie","doi":"10.2478/tmmp-2022-0013","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0013","url":null,"abstract":"Abstract In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δnm), where ℋ represents one of the spaces ℓ∞, c or c0.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {c, c0} will be given. Also, some matrix characterizations concerning these spaces will be computed. Moreover, the characterization of some classes of compact operators on the spaces ℓ∞(f, g, Δnm)and c0(f, g, Δnm)by employing the Hausdorff measure of non-compactness will be determined.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"81 1","pages":"165 - 182"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42161385","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}
Abstract In this article, we study the integrability and the non-existence of periodic orbits for the planar Kolmogorov differential systems of the form x˙=x(Rn-1(x,y)+Pn(x,y)+Sn+1(x,y)),y˙=y(Rn-1(x,y)+Qn(x,y)+Sn+1(x,y)), matrix{ {dot x = xleft( {{R_{n - 1}}left( {x,y} right) + {P_n}left( {x,y} right) + {S_{n + 1}}left( {x,y} right)} right),} hfill cr {dot y = yleft( {{R_{n - 1}}left( {x,y} right) + {Q_n}left( {x,y} right) + {S_{n + 1}}left( {x,y} right)} right),} hfill cr } where n is a positive integer, Rn−1, Pn, Qn and Sn+1 are homogeneous polynomials of degree n − 1, n, n and n + 1, respectively. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.
{"title":"Integrability and Non-Existence of Periodic Orbits for a Class of Kolmogorov Systems","authors":"Sarbast M. Hussein, T. Salhi, Bo Huang","doi":"10.2478/tmmp-2022-0011","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0011","url":null,"abstract":"Abstract In this article, we study the integrability and the non-existence of periodic orbits for the planar Kolmogorov differential systems of the form x˙=x(Rn-1(x,y)+Pn(x,y)+Sn+1(x,y)),y˙=y(Rn-1(x,y)+Qn(x,y)+Sn+1(x,y)), matrix{ {dot x = xleft( {{R_{n - 1}}left( {x,y} right) + {P_n}left( {x,y} right) + {S_{n + 1}}left( {x,y} right)} right),} hfill cr {dot y = yleft( {{R_{n - 1}}left( {x,y} right) + {Q_n}left( {x,y} right) + {S_{n + 1}}left( {x,y} right)} right),} hfill cr } where n is a positive integer, Rn−1, Pn, Qn and Sn+1 are homogeneous polynomials of degree n − 1, n, n and n + 1, respectively. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"81 1","pages":"145 - 154"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44051518","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}
B. S. Senthil Kumar, J. Rassias, S. Idir, S. Sabarinathan
Abstract The intention of this study is to present some stronger results by investigating Ulam-JRassias product stability and Ulam-JRassias mixed-type sum-product stability of a new reciprocal functional equation. Also, a suitable counter-example is presented to show the failure of stability result for the singular case.
{"title":"Stabilities and Non-Stabilities of a New Reciprocal Functional Equation","authors":"B. S. Senthil Kumar, J. Rassias, S. Idir, S. Sabarinathan","doi":"10.2478/tmmp-2022-0005","DOIUrl":"https://doi.org/10.2478/tmmp-2022-0005","url":null,"abstract":"Abstract The intention of this study is to present some stronger results by investigating Ulam-JRassias product stability and Ulam-JRassias mixed-type sum-product stability of a new reciprocal functional equation. Also, a suitable counter-example is presented to show the failure of stability result for the singular case.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"81 1","pages":"81 - 88"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43092741","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：