Iskanje po katalogu digitalne knjižnice

Opis: Optimizing cutting parameters in fiber laser cutting of austenitic stainless steel is challenging due to the complex interplay of multiple variables and quality metrics. To solve this problem, Latin hypercube sampling was used to ensure a comprehensive and efficient exploration of the parameter space with a smaller number of trials (185), coupled with feedforward neural networks for predictive modeling. The networks were trained with a leave-oneout cross-validation strategy to mitigate overfitting. Different configurations of hidden layers, neurons, and training functions were used. The approach was focused on minimizing dross and roughness on both the top and bottom areas of the cut surfaces. During the testing phase, an average MSE of 0.063 and an average MAPE of 4.68% were achieved by the models. Additionally, an experimental test was performed on the best parameter settings predicted by the models. Initial modelling was conducted for each quality metric individually, resulting in an average percentage difference of 1.37% between predicted and actual results. Grid search was also per formed to determine an optimal input parameter set for all outputs, with predictions achieving an average ac curacy of 98.34%. Experimental validation confirmed the accuracy and robustness of the model predictions, demonstrating the effectiveness of the methodology in optimizing multiple parameters of complex laser cutting processes.
Ključne besede: laser cutting optimization, cut surface quality, dross formation, Latin hypercube sampling, feedforward neural network
Objavljeno v DKUM: 10.01.2025; Ogledov: 0; Prenosov: 23
Celotno besedilo (3,38 MB)
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Opis: ▫$2$▫-pakirno število ▫$\rho_2(G)$▫ grafa ▫$G$▫ je kardinalnost največjega ▫$2$▫-pakiranja grafa ▫$G$▫, odprto pakirno število ▫$\rho^{\rm o}(G)$▫ pa kardinalnost največjega odprtega pakiranja grafa ▫$G$▫, kjer je odprto pakiranje (oz. ▫$2$▫ pakiranje) množica vozlišč grafa ▫$G$▫, katerih dve (zaprti) soseščini se ne sekata. Dokazano je, da če je ▫$G$▫ dvodelen, potem je ▫$\rho^{\rm o}(G\Box K_2) = 2\rho_2(G)$▫. Za hiperkocke sta določeni spodnji meji ▫$\rho_2(Q_n) \ge 2^{n - \lfloor \log n\rfloor -1}$▫ in ▫$\rho^{\rm o}(Q_n) \ge 2^{n - \lfloor \log (n-1)\rfloor -1}$▫. Te ugotovitve so uporabljene za injektivna barvanja hiperkock. Dokazano je, da je ▫$Q_9$▫ najmanjša hiperkocka, ki ni popolno injektivno obarvljiva. Dokazano je tudi, da je ▫$\gamma_t(Q_{2^k}\times H) = 2^{2^k-k}\gamma_t(H)$▫, kjer je ▫$H$▫ poljuben graf brez izoliranih vozlišč.
Ključne besede: 2-pakirno število, odprto pakirno število, dvodelna prizma, hiperkocke, injektivno barvanje, celotno dominacijsko število, 2-packing number, open packing number, bipartite prism, hypercube, injective coloring, total domination number
Objavljeno v DKUM: 28.02.2024; Ogledov: 260; Prenosov: 10
Povezava na celotno besedilo

Opis: Profil grafa ▫$G$▫ je poljubna neprazna multimnožica vozlišč iz ▫$G$▫. Pripadajoča funkcija oddaljenosti priredi vsakemu vozlišču iz ▫$V(G)$▫ vsoto razdalj do vozlišč iz profila. Najprej so dobljene nekatere uporabne lastnosti funkcije oddaljenosti na hiperkockah, nato pa je funkcija oddaljenosti obravnavana na poljubnih medianskih grafih glede na njihove izometrične vložitve v hiperkocke. V posebnem je najdena povezava med vozlišči medianskega grafa ▫$G$▫, katerega funkcija oddaljenosti je največja (antimedianska množica v ▫$G$▫), z antimediansko množico pripadajoče hiperkocke. Medtem ko je za lihe profile antimedianska množica neodvisna množica, ki leži na strogem robu medianskega grafa, obstajajo medianski grafi, v katerih določeni sodi profili porajajo konstantno funkcijo oddaljenosti. Take medianske grafe karakteriziramo na dva načina: kot grafe, katerih periferna transverzala je 2, in kot grafe z geodetskim številom 2. Nazadnje predstavimo algoritem, ki za dani graf ▫$G$▫ z ▫$n$▫ vozlišči in ▫$m$▫ povezavami v času ▫$O(m log n)$▫ odloči, ali je ▫$G$▫ medianski graf z geodetskim številom 2.
Ključne besede: hiperkocka, medianski graf, medianska množica, funkcija oddaljenosti, geodetsko število, periferna transverzala, median graph, median set, remoteness function, geodetic number, periphery transverzal, hypercube
Objavljeno v DKUM: 10.07.2015; Ogledov: 1297; Prenosov: 144
Povezava na celotno besedilo

Opis: Partial cubes are graphs isometrically embeddable into hypercubes. Three infinite families and a few sporadic examples of cubic partial cubes are known. The concept of a tribe is introduced as means to systematize the known examples and establish relations among them. Efficient methods of computation of tribes are developed and several concrete tribes, that include known, as well as new cubic partial cubes, are computed by hand and with the use of a computer.
Ključne besede: mathematics, graph theory, partial cube, hypercube, isometric embedding, tribe, algorithm
Objavljeno v DKUM: 10.07.2015; Ogledov: 1088; Prenosov: 182
Celotno besedilo (688,41 KB)
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Opis: The resonance graph ▫$R(B)$▫ of a benzenoid graph ▫$B$▫ has the perfect matchings of ▫$B$▫ as vertices, two perfect matchings being adjacent if their symmetric difference forms the edge set of a hexagon of ▫$B$▫. A family ▫$mathscr{P}$▫ of pair-wise disjoint hexagons of a benzenoid graph ▫$B$▫ is resonant in ▫$B$▫ if ▫$B -- mathscr{P}$▫ contains at least one perfect matching, or if ▫$B -- mathscr{P}$▫ is empty. It is proven that there exists a surjective map ▫$f$▫ from the set of hypercubes of ▫$R(B)$▫ onto the resonant sets of B such that a ▫$k$▫-dimensional hypercube is mapped into a resonant set of cardinality ▫$k$▫.
Ključne besede: matematika, teorija grafov, benzenoidni graf, popolno prirejanje, resonančni graf, hiperkocka, mathematics, graph theory, benzenoid graph, perfect matching, resonance graph, hypercube
Objavljeno v DKUM: 10.07.2015; Ogledov: 1589; Prenosov: 79
Povezava na celotno besedilo