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This paper studies the constrained two-dimensional non-guillotine cutting problem with defects, in which a set of items of a specific size is cut from a large rectangular sheet with defective areas, with the number of each type of cut item cannot exceed a specified quantity. The objective is to maximise the total value of the cut items. We propose a decomposition approach to address the problem. The process involves decomposing the original problem into a master problem and a subproblem. The master problem is formulated as a one-dimensional contiguous bin packing problem, while the subproblem is an x-Check problem to identify a two-dimensional packing that does not lead to any overlap. The x-Check problem is effectively addressed by using an integer linear programming model. When the x-Check problem proves infeasible, cuts are added to the master problem, and the iteration is repeated until the x-Check finds a feasible solution. Furthermore, we introduce several novel techniques, including valid inequalities, preprocessing techniques, and lifting the cut methods to improve the performance of the algorithm. Extensive computational results show that our method can quickly find the optimal solution for the 5450 instances in the literature. [ABSTRACT FROM AUTHOR]

In additive manufacturing processes such as laser powder bed fusion, the build orientation and packing of components affect the required support structures, the number of parts in each build, and the surface roughness of the printed parts, among other factors. Maximising the packing density while minimising the build height can increase effective machine utilisation and decrease per-part cost. Yet, the build layout optimisation problem is highly nonlinear and difficult to solve using human intuition, so a systematic algorithm approach is required. Here, we present and demonstrate a voxel-based analysis method with Bayesian optimisation for determining component build orientation in additive manufacturing. We introduce selected case studies incorporating exemplary process attributes of laser powder bed fusion, including the determination of orientation and packing configurations based on support removal and tool-accessibility constraints. [ABSTRACT FROM AUTHOR]

The Colored bin packing problem (CBPP) is a generalization of the Bin packing problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable neighborhood search (VNS) and a matheuristic approach that combines linear programming with the meta-heuristics VNS and Greedy randomized adaptive search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number of instances, even for those with many items. [ABSTRACT FROM AUTHOR]

Based on the packing density of cross-polytopes in R n , more than 50 years ago Golomb and Welch proved that the packing density of Lee spheres in Z n must be strictly smaller than 1 provided that the radius r of the Lee sphere is large enough compared with n, which implies that there is no perfect Lee code for the corresponding parameters r and n. In this paper, we investigate the lattice packing density of Lee spheres with fixed radius r for infinitely many n. First we present a method to verify the nonexistence of the second densest lattice packing of Lee spheres of radius 2. Second, we consider the constructions of lattice packings with density δ n → 2 r (2 r + 1) r ! as n → ∞ . When r = 2 , the packing density can be improved to δ n → 2 3 as n → ∞ . [ABSTRACT FROM AUTHOR]

En los últimos años, la industria del envasado ha comenzado a tomar conciencia sobre el impacto ambiental de los materiales utilizados en sus productos. El creciente interés de los consumidores por opciones más ecológicas ha llevado a la industria a enfocarse en la investigación y el desarrollo de alternativas que no solo sean más sostenibles, sino que mantengan y mejoren las características del producto, garantizando una mayor duración y seguridad alimentaria. Este artículo explora cómo algunos residuos biológicos provenientes de la cadena agrícola y agroindustrial, combinados con agentes antimicrobianos pueden ser aprovechados para crear empaques biodegradables, activos e inteligentes. Estos empaques no solo mejoran la calidad de los alimentos, sino que también ofrecen propiedades de barrera que ayudan a preservar su inocuidad hasta llegar al consumidor final.

Let i be a positive integer, an i -star denoted by S i is a complete bipartite graph K 1 , i. An { S 2 , S 3 } -packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum { S 2 , S 3 } -packing problem is to find an { S 2 , S 3 } -packing of a given graph containing the maximum number of vertices. The { S 2 , S 3 } -factor problem is to answer whether there is an { S 2 , S 3 } -packing containing all vertices of the given graph. The { S 2 , S 3 } -factor problem is NP-complete in cubic graphs. In this paper we design a quadratic-time algorithm for finding an { S 2 , S 3 } -packing of G that covers at least thirteen-sixteenths of its vertices with only a few exceptions. We also present some (2 , 3) -regular graphs with their maximum { S 2 , S 3 } -packings covering exactly thirteen-sixteenths of their vertices. [ABSTRACT FROM AUTHOR]

This paper studies the constrained two-dimensional guillotine cutting problem with defects, whose objective is to cut a subset of given items from a defective sheet such that the profit of selected items is maximised. The guillotine cut constraint, which requires each cut must go through one side of the sheet to the opposite side, is considered. We solve this problem via a recursive dynamic programming approach. A set of upper bounds is proposed to keep the promising nodes. The normal points and raster points are extended to reduce the number of vertical and horizontal cuts by considering the effect of the defect. The experiment results show that our approach can solve most of the instances in the literature and outperforms existing approaches. [ABSTRACT FROM AUTHOR]

The Tree Packing Conjecture (TPC) by Gyárfás states that any set of trees \(T_2,\dots,T_{n-1}, T_n\) such that \(T_i\) has \(i\) vertices pack into \(K_n\). The conjecture is true for bounded degree trees, but in general, it is widely open. Bollobás proposed a weakening of TPC which states that \(k\) largest trees pack. The latter is true if none tree is a star, but in general, it is known only for \(k=5\). In this paper we prove, among other results, that seven largest trees pack.

2,4-Difluoronitrobenzene has been reacted with a linker diamine (ethylenediamine or propylenediamine) and butylamine, in either order, to give new molecular building blocks for porous supramolecular networks. Two structures were established by X-ray single crystal structure determinations. The propylenediamine structure displays small pores, which may be due to the longer and more flexible linker in the structure. [ABSTRACT FROM AUTHOR]

This paper explores methods to improve the sustainability of packing artworks, focusing on soft wrapping of framed paintings. In 2022, the UK Museums and Heritage Sustainable Packing Group was formed. The research described in this paper focuses on one aspect of the group's activity: seeking to find materials and methods which reduce environmental burdens and comply with conservation standards for soft wrapping two-dimensional artworks for short journeys between display, storage locations and conservators' studios. The project investigated the physical qualities of recycled content polyethylene (PE), bioplastics and paper-based alternatives, along with common barrier materials such as virgin PE sheet and Bubble Wrap®, to form comparative datasets. Each material's environmental impact, potential for reuse, interaction with artworks and ability to maintain adequate buffering against environmental changes during transport was researched. Alternative methods were also explored to reduce the quantity of sealing tape and promote its reversibility and reuse. The environmental impacts of the materials were assessed by sustainability specialists at the University of Manchester's Sustainable Materials Innovation Hub. Reusable and recycled content films offered the most promising alternatives to the PE wrapping most used at present. The use of a tying method, eliminating the need for adhesive tape, also showed potential for further investigation. The low-cost testing methodology should be refined to better control the variables and allow for more repeatable testing, but these preliminary results will help to refine future research directions. [ABSTRACT FROM AUTHOR]

The Tree Packing Conjecture (TPC) by Gyárfás states that any set of trees T2,...,n-1, Tn Ti has i vertices pack into Kn. The conjecture is true for bounded degree trees, but in general, it is widely open. Bollobás proposed a weakening of TPC which states that k largest trees pack. The latter is true if none tree is a star, but in general, it is known only for k = 5. In this paper we prove, among other results, that seven largest trees pack. [ABSTRACT FROM AUTHOR]

Any collection of non-blocking cubes, whose total volume does not exceed 1/3, can be packed into the unit cube. [ABSTRACT FROM AUTHOR]

To solve the problem of high oxygen content in the deoxygenated pregnant liquid after long-term use of the deoxygenation tower in the zinc powder replacement process, this paper mainly conducts a series of studies on the packing types and loading methods of the deoxygenation tower in a gold smelting plant. Through in-depth comparison and analysis of multiple process indicators such as deoxygenation rate, replacement of barren liquid, and grade of gold mud, it was found that using polypropylene Pall Ring packing instead of plastic point wave packing can significantly alleviate the problem of clogging of gaps after calcium deposition of the packing, improve the deoxygenation performance of the deoxygenation tower, significantly reduce zine powder consumption, lower the grade of precious metals in replacement barren liquid, and improve the grade of gold mud. The improvement of packing has extended the service life of the deoxygenation tower, reduced the interference of base metal elements on the gold mud smelting process, and achieved significant economic benefits. [ABSTRACT FROM AUTHOR]

This study aims to evaluate the presence of residual Plus Moist HS-W (PM), a novel calcium alginate packing material, during the initial postoperative visit following endoscopic sinus surgery. The research aims to identify factors that influence the quantity of remaining PM. A retrospective review of medical records was conducted for patients who underwent middle meatus packing with PM. A total of fifty-two patients (representing 92 sides of paranasal sinuses) were included in the analysis. The remaining PM was classified as follows: absent (0) in 41 out of 92 cases, minimal (1) in 22 out of 92 cases, moderate (2) in 15 out of 92 cases, and substantial (3) in 14 out of 92 cases. Notably, all three patients who underwent Draf III surgery exhibited a significant amount of PM during their initial visit, with two patients classified as grade 2 and one patient as grade 3. Other factors investigated were found to be unrelated to the persistence of PM. Removal of all PM was achieved effortlessly using suction under flexible endoscopy. This study highlights the efficacy of PM in post-endoscopic sinus surgery care. It is important to limit an amount of PM, particularly in Draf III procedures. [ABSTRACT FROM AUTHOR]

The review and comparative analysis of known literature approaches and methods for predicting the packing density of binary powder systems are carried out. A theoretical model is proposed for a binary mixture to provide the spline approximation of calculated and research data with an appropriate accuracy. The model parameters are physical values, whose comparison for different binary systems makes it possible to estimate both the effect of a method of their formation on the packing density and the degree of adequacy to real powder materials for the available theoretical models. [ABSTRACT FROM AUTHOR]

High temperatures have dramatic negative effects on interconnect performance. In a bus, whenever the state transitions from "0" to "1", or "0" to "1", joule heating causes the temperature to rise. A low-power error-correcting cooling (LPECC) code, introduced in Chee et al. (IEEE Trans Inf Theory 64:3062–3085, 2018), is a coding scheme which can be used to control the peak temperature, the average power consumption of on-chip buses and error-correction for the transmitted information, simultaneously. In this paper, we show upper bounds and some lower bounds of LPECC codes by some combinatorial configurations, and also present several families of optimal LPECC codes. [ABSTRACT FROM AUTHOR]

This article compares two types of external ear canal packing options, Spongostan and Silastic, for endoscopic ear surgery. The study found that there was no statistically significant difference in post-operative healing outcomes between the two dressings. Both dressings were considered viable options for endoscopic ear surgery. The study aimed to fill a gap in the literature regarding packing options for this type of surgery. However, the study has limitations and further research is needed to determine the optimal timing of leaving the Spongostan dressing in place. [Extracted from the article]

In a graph G : = (V (G) , E (G)) , a subset M of the vertex set V (G) is a module (or interval, clan) of G if every vertex outside M is adjacent to all or none of M. The empty set, the singleton sets, and the full set of vertices are trivial modules. The graph G is indecomposable (or prime) if all its modules are trivial. If G is indecomposable, we say that an edge e of G is a removable edge if G − e is indecomposable (here G − e : = (V (G) , E (G) − { e })). The graph G is said to be unstable if it has no removable edges. For a positive integer k , the k th power G k of a graph G is the graph obtained from G by adding an edge between all pairs of vertices of G with distance at most k. A graph G of order n (i.e., | V (G) | = n) is said to be p -placeable into G k , if G k contains p edge-disjoint copies of G. In this paper, we answer a question, suggested by Boudabbous in a personal communication, concerning unstable graphs and packing into their fifth power as follows: First, we give a characterization of the unstable graphs which is deduced from the results given by Ehrenfeucht, Harju and Rozenberg (the theory of 2 -structures: a framework for decomposition and transformation of graphs). Second, we prove that every unstable graph G is 2 -placeable into G 5 . [ABSTRACT FROM AUTHOR]

An i-packing in a graph G is a set of vertices that are pairwise at distance more than i. A packing colouring of G is a partition X = {X1, X2,... , Xk } of V(G) such that each colour class Xi is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ(G). In this paper we investigate the existence of trees T for which there is only one packing colouring using χρ(T) colours. For the case χρ(T) = 3, we completely characterise all such trees. As a by-product we obtain sets of uniquely 3-χρ-packable trees with monotone χρ-colouring and non-monotone χρ-colouring respectively. [ABSTRACT FROM AUTHOR]

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In the MAXSPACE problem, given a set of ads A, one wants to place a subset A′ ⊆ A into K slots B1, ..., BK of size L. Each ad Ai ∈ A has sizesi and frequencywi. A schedule is feasible if the total size of ads in any slot is at most L, and each ad Ai ∈ A′ appears in exactly wi slots. The goal is to find a feasible schedule that maximizes the space occupied in all slots. We introduce MAXSPACE-RDWV, a MAXSPACE generalization with release dates, deadlines, variable frequency, and generalized profit. In MAXSPACE-RDWV each ad Ai has a release date ri ≥ 1, a deadline di ≥ ri, a profit vi that may not be related with si and lower and upper bounds wmini and wmaxi for frequency. In this problem, an ad may only appear in a slot Bj with ri ≤ j ≤ di, and the goal is to find a feasible schedule that maximizes the sum of values of scheduled ads. This paper presents some algorithms based on meta-heuristics GRASP, VNS, and Tabu Search for MAXSPACE and MAXSPACE-RDWV. We compare our proposed algorithms with Hybrid-GA proposed by Kumar et al. [Eur. J. Oper. Res. 173 (2006) 1067–1089]. We also created a version of Hybrid-GA for MAXSPACE-RDWV and compared it with our meta-heuristics. Some meta-heuristics like VNS and GRASP+VNS have better results than Hybrid-GA for both problems. In our heuristics, we apply a technique that alternates between maximizing and minimizing the fullness of slots to obtain better solutions. We also applied a data structure called BIT to the neighborhood computation in MAXSPACE-RDWV and showed that this enabled our algorithms to run more iterations. [ABSTRACT FROM AUTHOR]

This study aims to present alternatives to reduce the demand of cement in concrete production based on particle packing concepts. Physical and mechanical characteristics of concretes, as well as the resistance to chlorides action were analyzed. The tests conducted in this study included compressive strength, chloride migration, capillary absorption tests and wetting and drying cycles in 1M sodium chloride solution. Mixtures containing limestone filler presented satisfactory results compared to the reference mixture with particle packing. Excellent results were obtained for concrete with cement consumption of 253.34 kg.m-3 in terms of compressive strength, binder index, capillary absorption and depassivation time of rebars, thus reinforcing the concept that partial cement replacement by limestone filler yields positive results in these properties. Worse results were obtained for concrete with a cement consumption of 161.86 kg.m-3, because it had a higher proportion of filler than cement. The electrochemical monitoring of the steel bars also shows that the packing of the aggregates was essential to delay the initiation of corrosion.

Any collection of non-blocking four-dimensional cubes, whose total volume does not exceed 17/81, can be packed into the unit four-dimensional cube. This bound is tight for the parallel packing. [ABSTRACT FROM AUTHOR]

Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or paraboloids. Packing n-dimensional spheres into a minimum-height container bounded by a parabolic surface is formulated. The minimum allowable distances between spheres as well as between spheres and the container boundary are considered. A normalized Φ-function is used for analytical description of the containment constraints. A nonlinear programming model for the packing problem is provided. A solution algorithm based on the feasible directions approach and a decomposition technique is proposed. The computational results for problem instances with various space dimensions, different numbers of spheres and their radii, the minimal allowable distances and the parameters of the parabolic container are presented to demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Mixed-Team-Relay (MTR) triathlon is a novel Olympic discipline whose performance determinants and tactical behaviors have barely been studied. Additionally, a regulatory change has been made to the male and female relay order for the Paris 2024 Olympics. Therefore, this study aimed to determine the performance determinants and race dynamics as a function of competitive level on the new regulated MTR triathlon. Results from 129 national teams, (516 elite triathletes) across five MTR World Triathlon Series and two MTR European Championships in 2022 and 2023, were analyzed. Split times, average speeds, time behind the race leader (gap), partial and finishing positions, pack position as well as the rank positions of every segment, relay leg, and over-all race were computed. Decision tree analyses were conducted as a predictive method for the overall results, and correspondence analyses were conducted to examine the relationship between the different relay legs and segments and the finishing positions. The performance of the fourth leg was the most relevant for overall result (30%), as well as the fourth running leg (16%) and the female legs performance (7%). Medallist relay teams were characterized by displaying a differential speed lower than 0.5 and 0.83 km/h, respectively, from the best-ranking athletes in the Legs 1 and 4. Furthermore, staying in the front pack after the second swimming leg showed a great relationship with achieving a medal position. New MTR triathlon rules shift race dynamics, emphasizing individual efforts in cycling and swimming, while maintaining the crucial importance of running. [ABSTRACT FROM AUTHOR]

Four 1-D chain coordination polymers containing bent 1,1′-binaphthyl ligands were synthesised with NiII, CuII and AgI. The use of (R)-4,4′-(2,2′-diethoxy-[1,1′-binaphthalene]-6,6′)dipyridine as a ligand yielded isostructural 1-D looping chains with NiII and CuII, whereas the use of AgI yielded both linear and helical 1-D chains. Changing the dipyridyl coordination groups to dicarboxylates in (S)-6,6′-dicarboxyl-2,2′-diethoxy-1,1′-binaphthalene yielded a 1-D looping chain with a CuII paddlewheel motif. The AgI 1-D chain features two crystallographically distinct 1-D chain morphologies with a triple helix and linear strips. The packing arrangement of the 1-D chains differs because of the intermolecular interactions present, with the steric bulk of the ethoxy substituent on the 1,1′-binaphthyl enabling the formation of large void spaces. Chiral supramolecular compounds containing 1,1′-binapthyl are increasingly explored for chiroptical techniques including fluorescence-based sensing. Careful design of these compounds can yield systems with accessible voids and complimentary intermolecular interactions that can be tailored as a function of the 1,1′-binapthyl's steric hinderance and hydrogen bonding ability. (Image credit: Carol Hua.) [ABSTRACT FROM AUTHOR]

The characteristics of the plate fractionation tower and the packed fractionation tower in Fluid Catalytic Cracking Unit (FCCU) are briefly introduced in this paper. Technical renovation of the fractionation tower in FCCU of SINOPEC Cangzhou Company is also presented. The grading placement of packing and CTST tray was formed after the modification of top cycle tray, gasoline and diesel separation section tray replacement with packing. The pressure drop of fractionating tower was reduced from 0.049MPa to 0.041MPa, and the gasoline final distillation point was increased from 201.8℃ to 204.6℃, the overlap degree of gasoline and diesel oil was reduced, the fractionation precision was improved, the percent yield of gasoline was increased by 2.5%, and good economic benefit was obtained. After the revamp, no salt deposition occurred in the top section of the fractionation tower and the unit was in normal operation. [ABSTRACT FROM AUTHOR]

We prove that the ladder with 3 rungs and the house graph have the edge-Erdős–Pósa property, while ladders with 14 rungs or more have not. Additionally, we prove that the latter bound is optimal in the sense that the only known counterexample graph does not permit a better result. [ABSTRACT FROM AUTHOR]

The authors have developed an approach to modeling the layer-by-layer filling of the particular 3D volume with a combination of non-spherical and spherical powder particles of different fractional compositions. They have used the phi-function technique and constructed the mathematical model of the problem of packing regular and irregular freely moving objects. They also proposed the heuristic algorithm that uses nonlinear optimization for calculating packing density/porosity factor. The authors compared the results of numerical modeling with experimental data obtained for the mixture of spherical and polyhedral powders of titanium alloys. They have established that the percentage ratio of powder particles within the investigated fraction, obtained using the developed algorithm, corresponds with high accuracy to the experimental results. This finding indicates the possibility of using numerical modeling results instead of costly experimental studies. The use of mathematical modeling and optimization techniques in additive manufacturing makes it possible to improve the efficiency of each stage of the technological process, reduce the number of defective products, and rationally plan the consumption of energy and material resources. [ABSTRACT FROM AUTHOR]

In distributed storage systems, the utilization of locally repairable codes offers the potential to reduce the complexity and bandwidth required for repairs. This paper focuses on a scenario where each information symbol is associated with several distinct repair sets, each of which includes a single parity check symbol. By leveraging various combinatorial designs, such as resolvable balanced incomplete block designs and resolvable group divisible designs, we establish regular packings and resolvable packings for all alphabet sizes greater than a specified constant. These packings enable the construction of optimal locally repairable codes with multiple repair sets. Specifically, in the case where r = 4 , we successfully construct optimal locally repairable codes with multiple repair sets, provided that the code dimension k is greater than or equal to 277. [ABSTRACT FROM AUTHOR]

Handling potatoes individually or collectively in packages can create opportunities for potatoes to develop quality defects including blackspot and shatter bruise. Three trials were conducted to examine how handling packaged potatoes can influence the risk for physical damage including shatter and blackspot bruise. An impact recording device was used to record peak acceleration (max g-force) in common fresh market packaging options (boxes or bales) at four drop heights (15 to 91 cm) on to three different surface types. When boxed potatoes were dropped onto concrete or a plastic slip, the potatoes on the bottom of the box had the highest risk of damage (greater than 100 g-force). When drop heights were lowered, or when cushioning material was added to hard surfaces (e.g., wooden pallet on top of concrete floor), the risk for impact damage was decreased throughout the box. When palletizing boxed potatoes, the risk of bruise decreased after the first layer was stacked on the pallet. Drop heights need to be below 15 cm, especially when making the first layer in a palletized stack of packaged potatoes to reduce potential bruising. The risk of high peak accelerations was not seen in the dropped or stationary bales for any of the drop heights examined. This study provided information for educating personnel on handling packaged potatoes and determining situations in which robotic stacking equipment needs to be adjusted to lower drop heights of packaged potatoes. [ABSTRACT FROM AUTHOR]

We study the problem of perfect tiling in the plane and explore the possibility of tiling a rectangle using integral distinct squares. Assume a set of distinguishable squares (or equivalently a set of distinct natural numbers) is given, and one has to decide whether it can tile the plane or a rectangle or not. Previously, it has been proved that tiling the plane is not feasible using a set of odd numbers or an infinite sequence of natural numbers including exactly two odd numbers. The problem is open for different situations in which the number of odd numbers is arbitrary. In addition to providing a solution to this special case, we discuss some open problems to tile the plane and rectangles in this paper. [ABSTRACT FROM AUTHOR]

Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems. [ABSTRACT FROM AUTHOR]

We prove a quantitative version of the classical Tits’ alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geometric consequences, as uniform estimates on systole, diastole, algebraic entropy and critical exponent of the groups, will be presented. Finally we will study the behaviour of these group actions under limits, providing new examples of compact classes of metric spaces. [ABSTRACT FROM AUTHOR]