Journal articles: 'Tur\'{a}n problem'

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F�redi, Zolt�n. "On a Tur�n type problem of Erd�s." Combinatorica 11, no. 1 (March 1991): 75–79. http://dx.doi.org/10.1007/bf01375476.

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Shi, Y. G. "An analogue of problem 26 of P. Turán." Bulletin of the Australian Mathematical Society 53, no. 1 (February 1996): 1–12. http://dx.doi.org/10.1017/s000497270001666x.

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Explicit formulas for Cotes numbers of the Gaussian Hermite quadrature formula based on the zeros of the nth Chebyshev polynomial of the second kind and their asymptotic behaviour as n → ∞ are given. This provides an answer to an analogue of Problem 26 of Tur´n.

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Davoyan, Irina. "Possibilities of Using the Scratch Programming Environment at the First Stage of School Education (to the Problem Statement)." Primary Education 8, no. 5 (October 30, 2020): 30–32. http://dx.doi.org/10.12737/1998-0728-2020-30-32.

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The article discusses approaches to the use of the Scrath programming environment in the educational process of primary school. The methodological manuals of S.N. Tur, T.P. Bokuchava, O. N. Burtaeva, describing the methodology for teaching programming, and various educational programming environments: LightBot, Little Wizzard, RoboMind. The possibilities that open up when using the Scrath programming environment in solving the problems of forming information literacy of younger students, organizing their educational research activities, as well as positive socialization are evaluated.

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Kato, Tomonori, Kazushi Nomura, Fukuo Kondo, Masami Wakisaka, and Akira Komiya. "Analysis of Japanese Patients Treated with or without Long-Term Epirubicin Plus Ara-C Intravesical Instillation Therapy for Low-Grade Superficial Bladder Cancer." Scientific World Journal 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/325305.

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The high incidence of tumor recurrence following transurethral resection (TUR) represents a major problem encountered in the management of bladder cancer. This study examined the efficacy of intravesical chemotherapy in superficial bladder cancer. We retrospectively analyzed 90 Japanese cases with low-grade superficial transitional cell carcinoma (stage T1, grades 1 and 2) who were rendered tumor-free by TURBT (TUR of bladder tumor) and who thereafter were treated with or without intravesical chemotherapy. Among them, instillation was terminated in 2 patients due to adverse effects (severe but reversible chemical cystitis). Remaining 88 patients were divided into 2 groups according to therapy: the TURBT-only group(n=46), defined as patients treated with TURBT alone, and the Instillation group(n=42), defined as patients treated with weekly intravesical instillation therapies using epirubicin plus Ara-C. Recurrence-free rate was significantly higher in the Instillation group than in the TURBT-only group (p=0.02, HR = 0.457). The 5-year recurrence-free rate was 58.5% for the Instillation group and 38.6% for the TURBT-only group. Our instillation schedule represents the most intensive regimen among previously reported therapies and resulted in a 54.3% decrease in incidence of tumor recurrence. We believe that the results of this study could provide useful information on management of bladder cancer.

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Yin, Jianhua, and Guangming Li. "A note on the potential function of an arbitrary graph H." Filomat 34, no. 11 (2020): 3759–66. http://dx.doi.org/10.2298/fil2011759y.

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Given a graph H, a graphic sequence ? is potentially H-graphic if there is a realization of ? containing H as a subgraph. In 1991, Erd?s et al. introduced the following problem: determine the minimum even integer ?(H,n) such that each n-term graphic sequence with sum at least ?(H,n) is potentially H-graphic. This problem can be viewed as a ?potential? degree sequence relaxation of the Tur?n problems. Let H be an arbitrary graph of order k. Ferrara et al. [Combinatorica, 36(2016)687-702] established an upper bound on ?(H,n): if ? = ?(n) is an increasing function that tends to infinity with n, then there exists an N = N(?,H) such that ?(H,n)? ?~(H)n + ?(n) for any n ? N, where ?~(H) is a parameter only depending on the graph H. Recently, Yin [European J. Combin., 85(2020)103061] obtained a new upper bound on ?(H,n): there exists an M = M(k,?(H)) such that ?(H,n) ? ?~(H)n + k2-3k+4 for any n ? M. In this paper, we investigate the precise behavior of ?(H,n) for arbitrary H with ?~?(H)+1(H < ?~(H) or??(H)+1(H) ? 2, where ??(H)+1(H) = min{?F)|F is an induced subgraph of H and |V(F)|= ?(H) + 1} and ?~?(H)+1(H) = 2(k-?(H)-1)+??(H)+1(H)-1. Moreover, we also show that ?(H,n) = (k-?(H)-1)(2n-k+?(H))+2 for those H so that ??(H)+1(H) = 1,?~?(H)+1(H)=~?~(H),?~p(H) < ?~(H) for ?(H) + 2 ? p ? k and there is an F < H with |V(F)| = ?(H) + 1 and ?(F) = (12,0?(H)-1).

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XU, JINHUI, ZHIYONG LIN, YANG YANG, and RONALD BEREZNEY. "TRAVELING SALESMAN PROBLEM OF SEGMENTS." International Journal of Computational Geometry & Applications 14, no. 01n02 (April 2004): 19–40. http://dx.doi.org/10.1142/s0218195904001342.

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In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n ∊-separated segments in two dimensional space. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique5 for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n2( log n)O(1/∊2)) time to compute a (1+∊)-approximation with probability ≥l/2, and can be derandomized with an additional factor of O(n2).

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Bansal, M. S., and O. Eulenstein. "An Ω(n^2/ log n) Speed-Up of TBR Heuristics for the Gene-Duplication Problem." IEEE/ACM Transactions on Computational Biology and Bioinformatics 5, no. 4 (October 2008): 514–24. http://dx.doi.org/10.1109/tcbb.2008.69.

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MONGELLI, H., and S. W. SONG. "PARALLEL RANGE MINIMA ON COARSE GRAINED MULTICOMPUTERS." International Journal of Foundations of Computer Science 10, no. 04 (December 1999): 375–89. http://dx.doi.org/10.1142/s0129054199000277.

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Given an array of n real numbers A=(a0, a1, …, an-1), define MIN(i,j)= min {ai,…,aj}. The range minima problem consists of preprocessing array A such that queries MIN(i,j), for any 0≤i≤n-1 can be answered in constant time. Range minima is a basic problem that appears in many other important graph problems such as lowest common ancestor, Euler tour, etc. In this work we present a parallel algorithm under the CGM model (coarse grained multicomputer), that solves the range minima problem in O(n/p) time and constant number of communication rounds. The communication overhead involves the transmission of p numbers (independent of n). We show promising experimental results with speedup curves approximating the optimal for large n.

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Eremeev, Anton, and Yulia Kovalenko. "On solving Travelling Salesman Problem with Vertex Requisitions." Yugoslav Journal of Operations Research 27, no. 4 (2017): 415–26. http://dx.doi.org/10.2298/yjor161012003e.

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We consider the Travelling Salesman Problem with Vertex Requisitions where, for each position of the tour, at most two possible vertices are given. It is known that the problem is strongly NP-hard. The algorithm, we propose for this problem, has less time complexity compared to the previously known one. In particular, almost all feasible instances of the problem are solvable in O(n) time using the new algorithm, where n is the number of vertices. The developed approach also helps in fast enumeration of a neighborhood in the local search and yields an integer programming model with O(n) binary variables for the problem.

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JÁJÁ, JOSEPH, and KWAN WOO RYU. "AN OPTIMAL RANDOMIZED PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM." Parallel Processing Letters 06, no. 02 (June 1996): 187–93. http://dx.doi.org/10.1142/s0129626496000182.

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We describe a randomized parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O( log n) time using O(n) operations with high probability on the Priority CRCW PRAM. The previous best known algorithms run in O( log 2 n) time using O(n log 2 n) operations on the CREW PRAM and O( log n) time using O(n log log n) operations on the Arbitrary CRCW PRAM. The technique presented can be used to generate the Euler tour of a rooted tree optimally from the parent representation.

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ADAMASZEK, ANNA, ARTUR CZUMAJ, and ANDRZEJ LINGAS. "PTAS FOR k-TOUR COVER PROBLEM ON THE PLANE FOR MODERATELY LARGE VALUES OF k." International Journal of Foundations of Computer Science 21, no. 06 (December 2010): 893–904. http://dx.doi.org/10.1142/s0129054110007623.

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Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be [Formula: see text]-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, k = Ø( log n/ log log n). In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k ≤ 2 log δ n, where δ = δ(ε). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with Ø((k/ε)Ø(1)) points.

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BROWN, EVELYN C., CLIFF T. RAGSDALE, and ARTHUR E. CARTER. "A GROUPING GENETIC ALGORITHM FOR THE MULTIPLE TRAVELING SALESPERSON PROBLEM." International Journal of Information Technology & Decision Making 06, no. 02 (June 2007): 333–47. http://dx.doi.org/10.1142/s0219622007002447.

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The multiple traveling salesperson problem (MTSP) involves scheduling m > 1 salespersons to visit a set of n > m locations. Thus, the n locations must be divided into m groups and arranged so that each salesperson has an ordered set of cities to visit. The grouping genetic algorithm (GGA) is a type of genetic algorithm (GA) designed particularly for grouping problems. It has been successfully applied to a variety of grouping problems. This paper focuses on the application of a GGA to solve the MTSP. Our GGA introduces a new chromosome representation to indicate which salesperson is assigned to each tour and the ordering of the cities within each tour. We compare our method to standard GAs that employ either the one-chromosome or two-chromosome representation for MTSP. This research demonstrates that our GGA with its new chromosome representation is capable of solving a variety of MTSP problems from the literature and can outperform the traditional encodings of previously published GA methods.

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CHAKRABORTI, ANIRBAN. "THE EUCLIDEAN TRAVELLING SALESMAN PROBLEM: FREQUENCY DISTRIBUTION OF NEIGHBORS FOR SMALL-SIZE SYSTEMS." International Journal of Modern Physics C 12, no. 06 (July 2001): 857–63. http://dx.doi.org/10.1142/s0129183101002048.

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We have studied numerically the frequency distribution ρ(n) of the nth neighbour along the optimal tour in the Euclidean travelling salesman problem for N cities, in dimensions d = 2 and d = 3. We find there is no significant dependence of ρ(n) on either the number of cities N or the dimension d.

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Nikiforov, V. "Merging the A-and Q-spectral theories." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 81–107. http://dx.doi.org/10.2298/aadm1701081n.

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Let G be a graph with adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G: The signless Laplacian Q(G) of G is defined as Q(G):= A(G) +D(G). Cvetkovic called the study of the adjacency matrix the A-spectral theory, and the study of the signless Laplacian{the Q-spectral theory. To track the gradual change of A(G) into Q(G), in this paper it is suggested to study the convex linear combinations A_ (G) of A(G) and D(G) defined by A? (G) := ?D(G) + (1 - ?)A(G), 0 ? ? ? 1. This study sheds new light on A(G) and Q(G), and yields, in particular, a novel spectral Tur?n theorem. A number of open problems are discussed.

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Ulyanov, M. V., and M. I. Fomichev. "Research of Features of the Combined Algorithm for Solving the Asymmetric Traveling Salesman Problem." INFORMACIONNYE TEHNOLOGII 27, no. 1 (January 20, 2021): 3–8. http://dx.doi.org/10.17587/it.27.3-8.

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The exact algorithm that implements the Branch and Boimd method with precomputed tour which is calculated by Lin-Kernighan-Helsgaun metaheuristic algorithm for solving the Traveling Salesman Problem is concerned here. Reducing the number of decision tree nodes, which are created by the Branches and Bound method, due to a "good" precomputed tour leads to the classical balancing dilemma of time costs. A tour that is close to optimal one takes time, even when the Lin-Kernighan-Helsgaun algorithm is used, however it reduces the working time of the Branch and Bound method. The problem of determining the scope of such a combined algorithm arises. In this article it is solved by using a special characteristic of the individual Traveling Salesman Problem — the number of changes tracing direction in the search decision tree generated by the Branch and Bound Method. The use of this characteristic allowed to divide individual tasks into three categories, for which, based on experimental data, recommendations of the combined algorithm usage are formulated. Based on the data obtained in a computational experiment (in range from 30 to 45), it is recommended to use a combined algorithm for category III problems starting with n = 36, and for category II problems starting with n = 42.

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Mustafa Ali, Ruqaya, Alberto Trovato, David Couvin, Amina N. Al-Thwani, Emanuele Borroni, Fahim H. Dhaer, Nalin Rastogi, and Daniela M. Cirillo. "Molecular Epidemiology and Genotyping ofMycobacterium tuberculosisIsolated in Baghdad." BioMed Research International 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/580981.

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Tuberculosis (TB) remains a major health problem in Iraq but the strains responsible for the epidemic have been poorly characterized. Our aim was to characterize the TB strains circulating in Bagdad (Iraq). A total of 270Mycobacterium tuberculosiscomplex (MTBC) strains isolated between 2010 and 2011 from TB patients attending the Center of Chest and Respiratory diseases in Baghdad were analyzed by Spoligotyping. The analysis indicated that 94.1% of the isolates belong to known genotype clades: CAS 39.6%, ill-defined T clade 29.6%, Manu 7.4%, Haarlem 7%, Ural 4.1%, LAM 3.3%, X 0.7%, LAM7-TUR 0.7%, EAI 0.7%, S 0.7%, and unknown 5.9%. Comparison with the international multimarker database SITVIT2 showed that SIT 309 (CAS1-Delhi) and SIT1144 (T1) were the most common types. In addition, 44 strains were included in SITVIT2 database under 16 new Spoligotype International Types (SITs); of these, 6 SITs (SIT3346, SIT3497, SIT3708, SIT3790, SIT3791, and SIT3800) (n= 32 strains) were created within the present study and 10 were created after a match with an orphan in the database. By using 24-loci MIRU-VNTR-typing on a subset of 110 samples we found a high recent transmission index (RTI) of 33.6%. In conclusion, we present the first unifying framework for both epidemiology and evolutionary analysis ofM. tuberculosisin Iraq.

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Fraser, Egba Anwaitu, and Obikwelu R. Okonkwo. "GENETIC ALGORITHM APPROACH FOR OPTIMAL CYCLIC TOUR ROUND THE STATE CAPITALS IN NIGERIA’S NIGER DELTA REGION." International Journal of Research -GRANTHAALAYAH 9, no. 5 (May 31, 2021): 171–86. http://dx.doi.org/10.29121/granthaalayah.v9.i5.2021.3906.

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The classical traveling salesman problem(TSP) is simple to state but difficult a problem to solve. TSP seeks to determine the total distance or cost of visiting (n-1) cities or points and returning to the starting city or point. In this research, the Genetic Algorithm (GA) technique is utilized for solving the problem of finding the optimal tour around the nine Niger Delta state capitals in Nigeria which is an example of a traveling salesman problem. The partially mapped(PMX) crossover operator and the inversion mutation operator techniques were employed due to their simplicity. Genetic algorithms are evolutionary techniques used in solving optimization problems according to the survival of the fittest. The method does not provide an optimal exact solution, rather, it gives an approximated result in time. Data required for the tour were obtained from an online google map website where the distances between the state capitals and their coordinates (longitude and latitudes) were obtained. The MATLAB software which is suitable for scientific computations was used in coding the results show that the BB algorithm yielded an optimal tour of 1351km with a cyclic tour of (X3,1), (X1,9), (X9,6), (X6,8), (X8,4), (X4,7), (X7,5), (X5,2), (X2,3) and then (X3,1) after nine (9) iterations. Solving using the genetic algorithm with the four genetic parameters population size(N), maximum generation(G), crossover probability (Pc), and mutation probability(Pn) were used and set to 30; 10; 0.8; and 0.1 respectively yielded an optimal path of (8476125398) which is with an optimal tour of 1124.0KMs. genetic algorithm yielded an improved result.

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Warren, Richard H. "Generating Cyclic Permutations: Insights to the Traveling Salesman Problem." WSEAS TRANSACTIONS ON INFORMATION SCIENCE AND APPLICATIONS 18 (July 2, 2021): 68–72. http://dx.doi.org/10.37394/23209.2021.18.9.

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Some results for the traveling salesman problem (TSP) are known for a prime number of cities. In this paper we extend these results to an odd number of cities. For an odd integer n, we show that there is an algorithm that generates n – 1 cyclic permutations, called tours for the traveling salesman problem, which cover the distance matrix. The algorithm allows construction of a two-dimensional array of all tours for the TSP on an odd number of cities. The array has the following properties: (i) A tour on a vertical line in the array moves the salesman uniquely compared to all other tours on the vertical line. (ii) The sum of the lengths of all tours on a vertical line is equal to the sum of all non-diagonal elements in the distance matrix for the TSP.

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ELBASSIONI, KHALED, ALEKSEI V. FISHKIN, and RENÉ SITTERS. "APPROXIMATION ALGORITHMS FOR THE EUCLIDEAN TRAVELING SALESMAN PROBLEM WITH DISCRETE AND CONTINUOUS NEIGHBORHOODS." International Journal of Computational Geometry & Applications 19, no. 02 (April 2009): 173–93. http://dx.doi.org/10.1142/s0218195909002897.

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In the Euclidean traveling salesman problem with discrete neighborhoods, we are given a set of points P in the plane and a set of n connected regions (neighborhoods), each containing at least one point of P. We seek to find a tour of minimum length which visits at least one point in each region. We give (i) an O(α)-approximation algorithm for the case when the regions are disjoint and α-fat, with possibly varying size; (ii) an O(α3)-approximation algorithm for intersecting α-fat regions with comparable diameters. These results also apply to the case with continuous neighborhoods, where the sought TSP tour can hit each region at any point. We also give (iii) a simple O( log n)-approximation algorithm for continuous non-fat neighborhoods. The most distinguishing features of these algorithms are their simplicity and low running-time complexities.

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Haqiqi, Arghob Khofya, and Sabila Nurus Syarifa. "Keefektifan Model Problem Based Learning Berbantuan Video dalam Liveworksheets Terhadap Kemampuan Pemecahan Masalah Matematis Siswa." Jurnal Pendidikan Matematika (Kudus) 4, no. 2 (November 16, 2021): 193. http://dx.doi.org/10.21043/jmtk.v4i2.12048.

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Penelitian ini dilatarbelakangi karena rendahnya kemampuan siswa dalam memecahkan masalah dalam pembelajaran matematika. Oleh karena itu, untuk mengatasi masalah tersebut dilakukan penelitian dengan model Problem-Based Learning (PBL) berbantuan video dalam liveworksheets. Penelitian ini menggunakan metode eksperimen kuasi dengan desain penelitian pretest-posttest control group design. Populasi dalam penelitian ini terdiri dari kelas X TKR 1 - X TKR 3 pada salah satu Sekolah Menengah Kejuruan (SMK) di Kudus. Pemilihan sampel menggunakan teknik cluster random sampling didapatkan kelas X TKR 2 sebagai kelas eksperimen dan X TKR 3 sebagai kelas kontrol. Hasil pelaksanaan pembelajaran kelas eksperimen yang dimulai dengan pemberian masalah menunjukkan adanya peningkatan kemampuan pemecahan masalah matematis. Selain itu uji N gain menunjukkan peningkatan skor kelas eksperimen sebesar 63%, sedang kelas kontrol sebesar 49%. Berdasarkan pelaksanaan dan hasil analisis maka dapat disimpulkan model problem-based learning berbantuan video dalam liveworksheets efektif dengan kategori sedang.Temuan ini mengindikasikan bahwa model PBL berbantuan video dalam liveworksheets dapat dijadikan alternatif model pembelajaran untuk mengembangkan kemampuan pemecahan masalah matematis siswa. This research is motivated by the low ability of students to solve problems in learning mathematics. Therefore, to overcome this problem, research was carried out using a video-assisted Problem-Based Learning (PBL) model in live worksheets. This study uses a quasi-experimental method with a pretest-posttest control group design. The population in this study consisted of class X TKR 1 - X TKR 3 at one of the Vocational High Schools in Kudus. The sample selection using cluster random sampling technique obtained class X TKR 2 as the experimental class and X TKR 3 as the control class. The results of the implementation of the experimental class learning which began with giving problems showed an increase in mathematical problem-solving abilities. In addition, the N-gain test showed an increase in the score of the experimental class by 63% while the control class was 49%. Based on the results of the implementation and analysis, it can be concluded that the video-assisted problem-based learning model on student worksheets is effective in the medium category. These findings indicate that the video-assisted PBL model in live worksheets can be used as an alternative learning model to develop students' mathematical problem-solving abilities.

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Nurbiyanto, Eko. "IMPLEMENTASI PROBLEM BASED LEARNING UNTUK MENINGKATKAN HASIL BELAJAR SISWA KELAS XI JURUSAN TKR SMK NEGERI 2 YOGYAKARTA." Jurnal Pendidikan Vokasi Otomotif 2, no. 1 (November 1, 2019): 115–26. http://dx.doi.org/10.21831/jpvo.v2i1.28394.

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This research aims to increase students learning outcomes of class XI TKR 4 in the PKKR at SMK N 2 Yogyakarta through the application of the Problem Based Learning model. The types of this research are Classroom Action Research (CAR). The research data retrieval is on January 7, 2019 until February 9, 2019 at SMK N 2 Yogyakarta. The research was carried out in 2 cycles where each cycle was 2 times meeting. The research subjects were students of class XI TKR 4 on the Pemeliharaan Kelistrikan Kendaraan Ringan (PKKR) subjects in the 2018/2019 academic year with a total of 21 students. Data collection is done by test, observation, and documentation. Data processing is done quantitatively by seeing the implementation of the Problem Based Learning (PBL) model and learning outcomes in each cycle. The success criteria determined are minimum 80% of students have reached the Minimum Completion Criteria (KKM) which is a minimum value of 76.00. The results of this research showed that the application of the Problem Based Learning (PBL) model is able to increase the learning outcomes of students in class XI TKR 4 in PKKR subjects at SMK N 2 Yogyakarta. The percentage of student who achieve KKM increase to 66.67% in the first cycle and 85.71% in the second cycle.

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ESTIVILL-CASTRO, VLADIMIR, APICHAT HEEDNACRAM, and FRANCIS SURAWEERA. "FPT-ALGORITHMS FOR MINIMUM-BENDS TOURS." International Journal of Computational Geometry & Applications 21, no. 02 (April 2011): 189–213. http://dx.doi.org/10.1142/s0218195911003615.

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This paper discusses the κ-BENDS TRAVELING SALESMAN PROBLEM. In this NP-complete problem, the inputs are n points in the plane and a positive integer κ, and we are asked whether we can travel in straight lines through these n points with at most κ bends. There are a number of applications where minimizing the number of bends in the tour is desirable because bends are considered very costly. We prove that this problem is fixed-parameter tractable (FPT). The proof is based on the kernelization approach. We also consider the RECTILINEAR κ-BENDS TRAVELING SALESMAN PROBLEM, which requires that the line-segments be axis-parallel. 1 Note that a rectilinear tour with κ bends is a cover with κ-line segments, and therefore a cover by lines. We introduce two types of constraints derived from the distinction between line-segments and lines. We derive FPT-algorithms with different techniques and improved time complexity for these cases.

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Azar, Yossi. "Lower Bounds for Insertion Methods for TSP." Combinatorics, Probability and Computing 3, no. 3 (September 1994): 285–92. http://dx.doi.org/10.1017/s096354830000119x.

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We show that the random insertion method for the traveling salesman problem (TSP) may produce a tour Ω(log log n/log log log n) times longer than the optimal tour. The lower bound holds even in the Euclidean Plane. This is in contrast to the fact that the random insertion method performs extremely well in practice. In passing, we show that other insertion methods may produce tours Ω(log n/log log n) times longer than the optimal one. No non-constant lower bounds were previously known.

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Hart, Douglas. "Buck, N., Gordon, I. and Young, K., with Ermisch, J. and Mills, L., "The London Employment Problem" (Book Review)." Town Planning Review 58, no. 1 (January 1987): 95. http://dx.doi.org/10.3828/tpr.58.1.k4657637l9001008.

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Harrath, Youssef. "Three-Step Metaheuristic for the Multiple Objective Multiple Traveling Salesmen Problem." International Journal of Applied Metaheuristic Computing 11, no. 4 (October 2020): 130–48. http://dx.doi.org/10.4018/ijamc.2020100107.

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In this article, the multiple objective multiple Traveling Salesman Problem is considered. m salesmen have to visit n cities to perform some tasks each taking a given processing time. Two objectives are considered: balance the working loads of different salesmen and minimize their total traveled distance. To solve this NP-hard problem, a 3-phase metaheuristic was developed. In the first 2 phases, the principle of center of mass and a neighborhood search technique are used to assign the n cities to the m salesmen. In the third phase, a TSP solver was used to generate an optimal tour to every salesman using its assigned cities in phase 2. The metaheuristic was tested using TSP benchmarks of different sizes. The obtained results showed almost optimal load balancing for all tested instances and optimal tours in term of total traveled distances. A conducted comparison study showed that the proposed metaheuristic outperforms a recently published clustering algorithm for the workload objective.

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DUMITRESCU, ADRIAN. "THE TRAVELING SALESMAN PROBLEM FOR LINES AND RAYS IN THE PLANE." Discrete Mathematics, Algorithms and Applications 04, no. 04 (December 2012): 1250044. http://dx.doi.org/10.1142/s1793830912500449.

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In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present several linear-time approximation algorithms with improved ratios for these problems for two cases of neighborhoods that are (infinite) lines, and respectively, (half-infinite) rays. Along the way we derive a tight bound on the minimum perimeter of a rectangle enclosing an open curve of length L.

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Choi, Youngmin, and Paul M. Schonfeld. "Review of Length Approximations for Tours with Few Stops." Transportation Research Record: Journal of the Transportation Research Board 2676, no. 3 (October 28, 2021): 201–13. http://dx.doi.org/10.1177/03611981211049433.

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The shortest tour distance for visiting all points exactly once and returning to the origin is computed by solving the well-known traveling salesman problem (TSP). Owing to the large computational effort needed for optimizing TSP tours, researchers have developed approximations that relate the average length of TSP tours to the number of points, n, visited per tour. The existing approximations are used in transportation system planning and evaluation for estimating the distance for vehicles with large capacities (e.g., delivery trucks) where n is relatively large. However, the average TSP tour lengths would be inaccurately estimated if the approximations were derived for a wide range of n values since the tour lengths increase at a decreasing rate (i.e., with [Formula: see text]) as n increases. A comprehensive review is presented here of existing studies approximating TSP tour lengths for low n values, which have become important for some recently favored delivery alternatives (e.g., deliveries by bikes, drones, and robots).

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Massinanke, Sambourou, and Chao Zhu Zhang. "Application of Genetic Algorithm on Travelling Salesman Person." Advanced Materials Research 1048 (October 2014): 526–30. http://dx.doi.org/10.4028/www.scientific.net/amr.1048.526.

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GA (Genetic algorithm) is an optimization method based on operators (mutation and crossover) utilizing a survival of the fittest idea. They are utilized favorably in various problems. (TSP) Travelling salesman problem is one of the famous studied. TSP is a permutation problem in which the aim is to determine the shortest tour between n different points (cities), otherwise, the problem aims to find a route covering all cities where that the total distance is minimal. In this study a single salesman travels to each of the cities and close the loop by returning to the city he started, the aim of this study is to determine the minimum number of generations in which salesman does the minimum path, cities are chosen at random as initial population. The new generations are then created iteratively till the proper path is attained.

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Jasim, Sajjad Majeed, and Faez Hassan Ali. "Using Travelling Salesman Principle to Evaluate the Minimum Total Cost of the Iraqi Cities." Ibn AL-Haitham Journal For Pure and Applied Sciences 32, no. 3 (September 16, 2019): 95–108. http://dx.doi.org/10.30526/32.3.2286.

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The traveling salesman problem (TSP) is a well-known and important combinatorial optimization problem. The goal is to ï¬nd the shortest tour that visits each city in a given list exactly once and then returns to the starting city. In this paper we exploit the TSP to evaluate the minimum total cost (distance or time) for Iraqi cities. So two main methods are investigated to solve this problem; these methods are; Dynamic Programming (DP) and Branch and Bound Technique (BABT). For the BABT, more than one lower and upper bounds are be derived to gain the best one. The results of BABT are completely identical to DP, with less time for number of cities (n), 5 â‰¤ n â‰¤ 25. These results proof the efficiency of BABT compared with some good heuristic methods. We are suggesting some additional techniques to improve the computation time of BABT for n â‰¤ 80.

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Roy, Sharadindu, Prof Samer Sen Sarma, Soumyadip Chakravorty, and Suvodip Maity. "A COMPARATIVE STUDY OF VARIOUS METHODS OF ANN FOR SOLVING TSP PROBLEM." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 4, no. 1 (February 1, 2013): 19–28. http://dx.doi.org/10.24297/ijct.v4i1a.3029.

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Abstract This paper represents TSP (Travelling Salesman Problem) by using Artificial Neural Networks.A comparative study of various methods of ANN is shown here for solving TSP problem.The Travelling Salesman Problem is a classical combinational optimization problem, which is a simple to state but very difficult to solve. This problem is to find the shortest possible tour through a set of N vertices so that each vertex is visited exactly once. TSP can be solved by Hopfield Network, Self-organization Map, and Simultaneous Recurrent Network. Hopfield net is a fully connected network, where every vertex is connected with each other forwardly and backwardly. So starting the walk from a vertex we can travel all the other vertex exactly once and return to starting vertex again.

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Rangachari, P. K., and Usha Rangachari. "Matters of taste: bridging molecular physiology and the humanities." Advances in Physiology Education 39, no. 4 (December 2015): 288–94. http://dx.doi.org/10.1152/advan.00092.2015.

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Taste perception was the focus of an undergraduate course in the health sciences that bridged the sciences and humanities. A problem-based learning approach was used to study the biological issues, whereas the cultural transmutations of these molecular mechanisms were explored using a variety of resources (novels, cookbooks, and films). Multiple evaluation procedures were used: problem summaries and problem-solving exercises (tripartite problem-solving exercise) for the problem-based learning component and group tasks and individual exercises for the cultural issues. Self-selected groups chose specific tasks from a prescribed list of options (setting up a journal in molecular gastronomy, developing an electronic tongue, designing a restaurant for synesthetes, organizing a farmers' market, marketing a culinary tour, framing hedonic scales, exploring changing tastes through works of art or recipe books, and crafting beers for space travel). Individual tasks were selected from a menu of options (book reviews, film reviews, conversations, creative writing, and oral exams). A few guest lecturers (wine making, cultural anthropology, film analysis, and nutritional epidemiology) added more flavor. The course was rated highly for its learning value (8.5 ± 1.2, n = 62) and helped students relate biological mechanisms to cultural issues (9.0 ± 0.9, n = 62).

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Bompadre, Agustín, Moshe Dror, and James B. Orlin. "Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems." Journal of Applied Probability 44, no. 1 (March 2007): 259–78. http://dx.doi.org/10.1239/jap/1175267177.

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We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

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Bompadre, Agustín, Moshe Dror, and James B. Orlin. "Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems." Journal of Applied Probability 44, no. 01 (March 2007): 259–78. http://dx.doi.org/10.1017/s0021900200002850.

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We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

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Dotsev, Arsen V., Andrey N. Rodionov, Veronika R. Kharzinova, Sergey N. Petrov, Dmitry G. Medvedev, Vugar A. Bagirov, Gottfried Brem, and Natalia A. Zinovieva. "An Assessment of Applicability of SNP Chip Developed for Domestic Goats in Genetic Studies of Caucasian Tur (Capra caucasica)." Diversity 13, no. 7 (July 8, 2021): 312. http://dx.doi.org/10.3390/d13070312.

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Caucasian tur (Capra caucasica) is native to Greater Caucasus Mountain Chain from Azerbaijan and Georgia in the East to Krasnodar region of Russia in the West. This species is divided into two subspecies (by some authors into species) —East-Caucasian tur and West-Caucasian tur and a subpopulation referred to as Mid-Caucasian tur. Up to date most of the genetic studies of Caucasian tur are based on mitochondrial DNA sequences and comprehensive investigation based on nuclear DNA is required for clarification of its genetic diversity and population structure. In our work, we assessed the applicability of Illumina Goat SNP50 BeadChip for genetic studies of Caucasian tur. Total of 15 specimens of Capra caucasica including East-Caucasian tur from Dagestan (E_TUR, n = 5), West-Caucasian tur from Karachay-Cherkessia (W_TUR, n = 5), and Mid-Caucasian tur from Kabardino-Balkaria (M_TUR, n = 5) were genotyped. After quality control, 5544 polymorphic loci, which were distributed all over 29 autosomes, were detected. The lowest number of SNPs was found on the 25th chromosome—68, and the highest on the 1st chromosome—348. It was shown that all the three groups of Caucasian tur clustered separately. A total of 2061 SNPs were common for all the populations, 594 were found only in W_TUR, 689 in E_TUR, and 530 in M_TUR. Individual heterozygosity ranged from 0.273 to 0.282 in W_TUR, from 0.217 to 0.253 in E_TUR, and from 0.255 to 0.283 in M_TUR. A clinal pattern of genetic variation was revealed. It was suggested to consider Caucasian tur a single species with several ecotypes. Thus, in our study we demonstrated that the Illumina Goat SNP50 BeadChip developed for domestic goats can be used as a useful tool for genetic studies of Caucasian tur.

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Wendi, Saputra, and Martias Martias. "Upaya Peningkatan Hasil Belajar Pemeliharaan Mesin Kendaraan Ringan dengan Model Pembelajaran Problem Based Learning (PBL)." MSI Transaction on Education 2, no. 4 (December 17, 2021): 183–92. http://dx.doi.org/10.46574/mted.v2i4.71.

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Penelitian bertujuan untuk mengetahui berapa besar peningkatan hasil belajar siswa pada mata pelajaran pemeliharaan mesin kendaraan ringan melalui penerapan model pembelajaran Problem Based Learning (PBL) pada siswa kelas XI program Keahlian Teknik Kendaraan Ringan (TKR) SMKN 2 Lubuk Basung tahun ajaran 2019/2020. Pendekatan yang digunakan dalam penelitian ini adalah pendekatan kualitatif dengan jenis penelitiannya adalah penelitian tindakan kelas. Penelitian terdiri dari dua siklus yang terdiri atas kegiatan perencanaan, pelaksanaan tindakan, pengamatan dan refleksi. Hasil penelitian menunjukkan bahwa terdapat peningkatan hasil belajar siswa pada mata pelajaran pemeliharaan mesin kendaraan ringan melalui penerapan model pembelajaran Problem Based Learning (PBL) pada siswa kelas XI program Keahlian Teknik Kendaraan Ringan (TKR) SMKN 2 Lubuk Basung tahun ajaran 2019/2020 dari siklus I rata-rata sebesar 67,89 meningkat pada siklus II menjadi 82,50%. Dari hasil penelitian maka dapat dikatakan bahwa metode PBL yang diterapkan dapat meningkatkan hasil belajar siswa khususnya untuk pemeliharaan mesin kendaraan ringan pada SMK N 2 Lubuk Basung.

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Dzuyev, R. I., A. Kh Sharipovа, A. R. Dzuev, A. A. Yevgajukovа, M. R. Tembotova, and F. H. Zhilyaeva. "Karyotaxonomic characteristics of the forest dormouse (Dryomys nitedula) in the North Caucasus." REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES 20, no. 3 (2020): 38–41. http://dx.doi.org/10.47928/1726-9946-2020-20-3-38-41.

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For the first time, the chromosome set is described in 4 subspecies of the forest Dormouse (Dryomys nitedula caucasicum Ogn. et. Tur.; D. n. tanaiticus Ogn.et Tur.; D. n. ognevi Hept. et Form. u D.n. dagestanicum Ogn. et Tur.) on the territory of the North Caucasus. A brief description of the features of the karyotype of the forest Dormouse is given.

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Voßen, Werner, Regine Fuchs, Kambiz Taraz, and Herbert Budzikiewicz. "Can the Peptide Chain of a Pyoverdin be Bound by an Ester Bond to the Chromophore? - The Old Problem of Pseudobactin 7SR1." Zeitschrift für Naturforschung C 55, no. 3-4 (April 1, 2000): 153–64. http://dx.doi.org/10.1515/znc-2000-3-405.

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Abstract The structure which had been proposed for the pyoverdin named pseudobactin 7SR1 (Yang and Leong, 1984) differed from those of all other pyoverdins investigated sofar: its peptide chain was supposedly linked to the chromophore not by an amide bond originating from its N-terminal amino acid, but rather by an ester bond involving one of the three Ser. It will be shown that the peptide chain of pseudobactin 7SR1 is actually bound to the chromophore amidically by its N-terminal Ser and that it comprises a cyc/odepsipeptidic substructure with an ester bond between the C-terminal Thr and the OH-group of the second Ser in the chain.

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Del Giudice, Francesco, Gian Maria Busetto, Martin S. Gross, Martina Maggi, Alessandro Sciarra, Stefano Salciccia, Matteo Ferro, et al. "Efficacy of three BCG strains (Connaught, TICE and RIVM) with or without secondary resection (re-TUR) for intermediate/high-risk non-muscle-invasive bladder cancers: results from a retrospective single-institution cohort analysis." Journal of Cancer Research and Clinical Oncology 147, no. 10 (March 6, 2021): 3073–80. http://dx.doi.org/10.1007/s00432-021-03571-0.

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Abstract Purpose (I) To evaluate the clinical efficacy of three different BCG strains in patients with intermediate-/high-risk non-muscle-invasive bladder cancer (NMIBC). (II) To determine the importance of performing routine secondary resection (re-TUR) in the setting of BCG maintenance protocol for the three strains. Methods NMIBCs who received an adjuvant induction followed by a maintenance schedule of intravesical immunotherapy with BCG Connaught, TICE and RIVM. Only BCG-naïve and those treated with the same strain over the course of follow-up were included. Cox proportional hazards model was developed according to prognostic factors by the Spanish Urological Oncology Group (CUETO) as well as by adjusting for the implementation of re-TUR. Results n = 422 Ta-T1 patients (Connaught, n = 146; TICE, n = 112 and RIVM, n = 164) with a median (IQR) follow-up of 72 (60–85) were reviewed. Re-TUR was associated with improved recurrence and progression outcomes (HRRFS: 0.63; 95% CI 0.46–0.86; HRPFS: 0.55; 95% CI 0.31–0.86). Adjusting for CUETO risk factors and re-TUR, BGC TICE and RIVM provided longer RFS compared to Connaught (HRTICE: 0.58, 95% CI 0.39–0.86; HRRIVM: 0.61, 95% CI 0.42–0.87) while no differences were identified between strains for PFS and CSS. Sub-analysis of only re-TUR cases (n = 190, 45%) showed TICE the sole to achieve longer RFS compared to both Connaught and RIVM. Conclusion Re-TUR was confirmed to ensure longer RFS and PFS in intermediate-/high-risk NMIBCs but did not influence the relative single BCG strain efficacy. When routinely performing re-TUR followed by a maintenance BCG schedule, TICE was superior to the other strains for RFS outcomes.

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Ghaffari, Aida, Maryam Rafraf, Roya Navekar, Bita Sepehri, Mohammad Asghari-Jafarabadi, and Seyyed-Mostafa Ghavami. "Turmeric and chicory seed have beneficial effects on obesity markers and lipid profile in non-alcoholic fatty liver disease (NAFLD)." International Journal for Vitamin and Nutrition Research 89, no. 5-6 (November 2019): 293–302. http://dx.doi.org/10.1024/0300-9831/a000568.

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Abstract. In an attempt to investigate new strategies aimed at reducing risk factors of non-alcoholic fatty liver disease (NAFLD), effects of turmeric (Curcuma longa L.) and chicory seed (Cichorium intybus L.) supplementation was evaluated in these patients. In this double-blind, randomized, controlled clinical trial, 92 patients with NAFLD aged 20–60 year with body mass index (BMI) ranged 24.9–40 kg/m2 was randomly assigned to 4 groups as follows. 1) Turmeric supplementation (3 g/d) (n = 23, TUR); 2) Chicory seed supplementation (infused 9 g/d (4.5 g /100mL)) (n = 23, CHI); 3) Turmeric and chicory seed supplementation (3 g/d turmeric + infused 9 g/d chicory seed (n = 23, TUR + CHI); 4) Placebo (n = 23, PLA). All intervention periods were 12 weeks. Fasting blood samples, anthropometric measurements, dietary records and physical activity were collected at baseline and at the end of the trial. Significant decreases were observed in BMI and waist circumference (WC) of subjects in CHI and TUR + CHI groups, compared with PLA group (p < 0.05). Combination of turmeric and chicory seed significantly decreased serum alkaline phosphatase level (p < 0.05). Serum levels of HDL-C increased considerably in TUR and TUR + CHI groups (p < 0.05 vs. placebo). Turmeric supplementation alone and plus chicory seed led to significant reduction in serum levels of TG/HDL-C and LDL-C/HDL-C ratio in TUR and TUR + CHI groups in comparison with placebo (p < 0.05). In conclusion, turmeric and chicory seed supplementation can be significantly useful in management of NAFLD risk factors.

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Grabner, Peter J. "Erd�s-Tur�n type discrepancy bounds." Monatshefte f�r Mathematik 111, no. 2 (June 1991): 127–35. http://dx.doi.org/10.1007/bf01332351.

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Koll�r, J�nos, Lajos R�nyai, and Tibor Szab�. "Norm-graphs and bipartite tur�n numbers." Combinatorica 16, no. 3 (September 1996): 399–406. http://dx.doi.org/10.1007/bf01261323.

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Hwang, Michael J., Ashish M. Kamat, Colin P. Dinney, Bogdan Czerniak, and Charles C. Guo. "Bladder Cancer Involving Smooth Muscle of Indeterminate Type or Muscularis Mucosae in Transurethral Biopsy Specimens." American Journal of Clinical Pathology 154, no. 2 (April 7, 2020): 208–14. http://dx.doi.org/10.1093/ajcp/aqaa030.

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Abstract Objectives Bladder cancers invading the muscularis mucosae (MM) are treated differently from those invading the muscularis propria (MP). However, it may be difficult to determine the type of smooth muscle in transurethral resection (TUR) or biopsy specimens. We aimed to investigate the clinicopathologic features of bladder cancers involving smooth muscle of indeterminate type (SMIT) in TUR specimens in comparison with those invading the MM. Methods We identified 103 patients with bladder cancer involving SMIT (n = 27) or the MM (n = 76) in TUR specimens. All patients underwent subsequent restaging TUR or cystectomy. Results Bladder cancer with SMIT invasion showed a significantly higher rate of MP invasion in the subsequent specimens than those invading the MM (52% vs 29%). Lack of MP in the TUR specimens had a significantly higher risk of MP invasion in the subsequent specimens than those with the MP (61% vs 40%). The overall survival time for patients with SMIT invasion was significantly shorter than those with MM invasion. Conclusions Bladder cancers with SMIT invasion in TUR specimens show more frequent cancer upstaging in the subsequent specimens and a poorer clinical outcome than those invading the MM, which highlights the importance of a cancer restaging procedure for these patients.

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Strauss, Danie. "Boundaries: an Interdisciplinary (Hi)Story." Koers - Bulletin for Christian Scholarship 81, no. 2 (October 31, 2016): 80–89. http://dx.doi.org/10.19108/koers.81.2.2273.

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The experience and awareness of boundaries forms an integral part of being human. This article investigates the systematic philosophical underpinnings of our understanding of the nature of boundaries, in some instances supported by historical considerations. It stands to reason that boundaries are related to our awareness of spatial relationships, even though this awareness cannot avoid incorporating the distinction between entities and properties, reflected in the distinction between the concrete what and the how of reality. Differences between the original (mathematical) meaning of space and other contexts within which we encounter analogies of spatial boundaries are considered by paying attention to the problem of accounting for physical space (which is neither continuous nor infinitely divisible), biotic and sensory space (compare notions such as Umwelt, ambient and environment) as well as the significance of closed and open systems also for inter-human relationships displaying a solidary unitary character, analogous to thermodynamic open systems. Boundaries between different modes of explanation finally underscore the typical on-going task of philosophy, namely to investigate boundary questions. It will be argued that the problem of the multivocal nature of the term boundary only finds a satisfactory solution if it is embedded in a non-reductionist ontology. Die ervaring van grense vorm ‘n integrale deel van menswees. Hierdie artikel ondersoek die sistematies-wysgerige onderbou van ons verstaan van die aard van grense. In sommige gevalle word hierdie ondersoek ondersteun deur oorwegings uit die geskiedenis van die filosofie en die vakwetenskappe. Dit spreek vanself dat grense verband hou met ons besef van ruimteverhoudinge, selfs al kan hierdie besef nie ontkom aan die onderskeiding tussen entiteite en hul eienskappe, soos wat dit gereflekteer word in die onderskeid tussen die konkrete wat en die hoe van die werklikheid nie. Verskille tussen die oorspronklike (wiskundige) sin van ruimte en ander kontekste waarin analogieë van die aard van ruimtelike grense ter sprake kom, word in oënskou geneem deur die probleem aan die orde te stel van hoe ons rekenskap moet gee byvoorbeeld van fisieke ruimte (wat nie kontinu en oneindig verdeelbaar is nie), biotiese en sensitiewe ruimte (bedink terme oos Umwelt, “ambient” en omgewing), asook die betekenis van geslote en oop sisteme, ook vir die aard van inter-menslike relasies wat oor ‘n solidêre eenheidskarakter beskik, analoog aan termodinamiese oop sisteme. Die grense tussen verskillende verklaringsmodi belig die voortgaande taak van die filosofie om rekenskap van grensvrae te gee. Die argument wat gevoer word loop uit op die gevolgtrekking dat die probleem van ‘n meersinnige gebruik van terme soos grense slegs tot ‘n bevredigende oplossing gebring kan word indien hierdie probleem in ‘n niereduksionistiese ontologie ingebed word.

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Borchardt, Frank. "Tur(n)ing the Tables: A Quiet Polemic." CALICO Journal 4, no. 4 (January 14, 2013): 31–35. http://dx.doi.org/10.1558/cj.v4i4.31-35.

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Bir�, A., and T. Szamuely. "A Tur�n-Kubilius inequality with multiplicative weights." Acta Mathematica Hungarica 70, no. 1-2 (1996): 39–56. http://dx.doi.org/10.1007/bf00113912.

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Ahmed, Zakir Hussain, Asaad Shakir Hameed, and Modhi Lafta Mutar. "Hybrid Genetic Algorithms for the Asymmetric Distance-Constrained Vehicle Routing Problem." Mathematical Problems in Engineering 2022 (June 22, 2022): 1–20. http://dx.doi.org/10.1155/2022/2435002.

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We aim to suggest a simple genetic algorithm (GA) and other four hybrid GAs (HGAs) for solving the asymmetric distance-constrained vehicle routing problem (ADVRP), a variant of vehicle routing problem (VRP). The VRP is a difficult NP-hard optimization problem that has numerous real-life applications. The VRP aims to find an optimal tour that has least total distance (or cost) to provide service to n customers (or nodes or cities) utilizing m vehicles so that every vehicle starts journey from and ends journey at a depot (headquarters) and visits every customer only once. The problem has many variations, and we consider the ADVRP for this study, where distance traveled by every vehicle must not exceed a predefined maximum distance. The proposed GA uses random initial population followed by sequential constructive crossover and swap mutation. The HGAs enhance the initial solution using 2-opt search method and incorporate a local search technique along with an immigration procedure to obtain effective solution to the ADVRP. Experiments have been conducted among the suggested GAs by solving several restricted and unrestricted ADVRP instances on asymmetric TSPLIB utilizing several vehicles. Our experiments claim that the suggested HGAs using local search methods are very effective. Finally, we reported a comparative study between our best HGA and a state-of-the-art algorithm on asymmetric capacitated VRP and found that our algorithm is better than the state-of-the-art algorithm for the instances.

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Helvetia, Tania, Nizwardi Jalinus, and Refdinal Refdinal. "ENGARUH MODEL PEMBELAJARAN PROBLEM SOLVING DAN MOTIVASI BERPRESTASI TERHADAP HASIL BELAJAR FISIKA SISWA SMK NEGERI 1 LAHAT." JURNAL PENDIDIKAN TEKNOLOGI KEJURUAN 1, no. 3 (August 30, 2018): 111–17. http://dx.doi.org/10.24036/jptk.v1i3.2023.

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Penelitian ini berawal dari masalah banyaknya mahasiswa yang memperoleh nilai rendah pada mata pelajaran fisika. Tujuan penelitian ini adalah untuk mengetahui pengaruh metode pembelajaran dan motivasi berprestasi terhadap hasil belajar pada mata pelajaran fisika pada siswa SMK N 1 Lahat. Jenis penelitian ini adalah quasi eksperimen menggunakan desain faktorial 2×2, yakni dengan memperhatikan kemungkinan adanya variabel moderator yang mempengaruhi penelitian (independent variable) terhadap hasil (dependent variable). Populasi dalam penelitian ini adalah siswa kelas X yang berjumlah 587 orang. Sampel dalam penelitian ini adalah siswa kelas X TSM 1 untuk kelas eksperimen dan X TKR 1 untuk kelas kontrol dengan pertimbangan kelas tersebut memiliki tingkat kemampuan sama. Kelas X TSM 1 diberikan metode pembelajaran problem solving sedangkan kelas X TKR 1 diberikan metode pembelajaran konvensional. Teknik yang digunakan untuk menganalisis data hasil penelitian dengan menggunakan teknik anova dua jalur. Hasil penelitian ini membuktikan bahwa: a) rata-rata hasil belajar siswa yang diajarkan dengan metode problem solving, lebih tinggi dibandingkan dengan rata-rata hasil belajar siswa yang diajarkan dengan menggunakan metode pembelajaran konvensional, b). Rata-rata hasil belajar mata pelajaran fisika memiliki motivasi berprestasi lebih tinggi dibandingkan dengan rata – rata hasil belajar siswa memiliki motivasi rendah, c) terdapat interaksi antara metode pembelajaran dan motivasi berprestasi dalam mempengaruhi hasil belajar siswa di dalam mata pelajaran fisika.

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Feng, Liquan, and Yumei Hu. "The Turán number of the graph 3P5." Filomat 34, no. 10 (2020): 3395–410. http://dx.doi.org/10.2298/fil2010395f.

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The Tur?n number ex(n,H) of a graph H, is the maximum number of edges in a graph of order n which does not contain H as a subgraph. Let Ex(n,H) denote all H-free graphs on n vertices with ex(n,H) edges. Let Pi denote a path consisting of i vertices, and mPi denote m disjoint copies of Pi. In this paper, we give the Tur?n number ex(n,3P5) for all positive integers n, which partly solve the conjecture proposed by L. Yuan and X. Zhang [7]. Moreover, we characterize all extremal graphs of 3P5 denoted by Ex(n, 3P5).

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Baricz, Árpád, Ali Bhayo, and Matti Vuorinen. "Turán type inequalities for generalized inverse trigonometric functions." Filomat 29, no. 2 (2015): 303–13. http://dx.doi.org/10.2298/fil1502303b.

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In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Tur?n type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur?n type inequality for a series considered by Ramanujan, involving the digamma function.

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Mihic, Ljubica, Aleksandar Pejcev, and Miodrag Spalevic. "Error estimations of Turán formulas with Gori-Micchelli and generalized Chebyshev weight functions." Filomat 32, no. 20 (2018): 6927–36. http://dx.doi.org/10.2298/fil1820927m.

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Abstract:

S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Tur?n formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Tur?n formula that has all its nodes real and belonging to the interval of integration, [-1,1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Tur?n quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1,1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.

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