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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.

The use of stem cells for tissue regeneration is a prominent trend in regenerative medicine and tissue engineering. In particular, dental pulp stem cells (DPSCs) have garnered considerable attention. When exposed to specific conditions, DPSCs have the ability to differentiate into osteoblasts and odontoblasts. Scaffolds are critical for cell differentiation because they replicate the 3D microenvironment of the niche and enhance cell adhesion, migration, and differentiation. The purpose of this study is to present the biological responses of human DPSCs to a purified 3D chitin scaffold derived from the marine demosponge Aplysina fistularis and modified with hydroxyapatite (HAp). Responses examined included proliferation, adhesion, and differentiation. The control culture consisted of the human osteoblast cell line, hFOB 1.19. Electron microscopy was used to examine the ultrastructure of the cells (transmission electron microscopy) and the surface of the scaffold (scanning electron microscopy). Cell adhesion to the scaffolds was determined by neutral red and crystal violet staining methods. An alkaline phosphatase (ALP) assay was used for assessing osteoblast/odontoblast differentiation. We evaluated the expression of osteogenic marker genes by performing ddPCR for ALP, RUNX2, and SPP1 mRNA expression levels. The results show that the chitin biomaterial provides a favorable environment for DPSC and hFOB 1.19 cell adhesion and supports both cell proliferation and differentiation. The chitin scaffold, especially with HAp modification, isolated from A. fistularis can make a significant contribution to tissue engineering and regenerative medicine.

This paper, the second part of a comprehensive Vilamovian bibliography, contains a list of 89 publications (1945–2000 and 2020–2022) concerning the history, culture and language of Wilamowice, a small town in the south of Poland, populated by descendants of medieval colonists of Germanic origin. The town is well known for its unusual folk costume and the critically endangered minority language known as Wymysorys. Although the bibliography mainly covers academic works (monographs, book chapters and journal articles) and popular science publications, it also includes a section listing literary works published in Wymysorys. Each entry provides bibliographic information, keywords and a brief description of the publication. Additionally, links to online versions of the works are provided where possible.

Nucleobindin-2 (Nucb2) is a protein that has been suggested to play roles in a variety of biological processes. Nucb2 contains two Ca2+/Mg2+-binding EF-hand domains separated by an acidic amino acid residue-rich region and a leucine zipper. All of these domains are located within the C-terminal half of the protein. At the N-terminal half, Nucb2 also possesses a putative Zn2+-binding motif. In our recent studies, we observed that Nucb2 underwent Ca2+-dependent compaction and formed a mosaic-like structure consisting of intertwined disordered and ordered regions at its C-terminal half. The aim of this study was to investigate the impact of two other potential ligands: Mg2+, which possesses chemical properties similar to those of Ca2+, and Zn2+, for which a putative binding motif was identified. In this study, we demonstrated that the binding of Mg2+ led to oligomerization state changes with no significant secondary or tertiary structural alterations of Nucb2. In contrast, Zn2+ binding had a more pronounced effect on the structure of Nucb2, leading to the local destabilization of its N-terminal half while also inducing changes within its C-terminal half. These structural rearrangements resulted in the oligomerization and/or aggregation of Nucb2 molecules. Taken together, the results of our previous and current research help to elucidate the structure of the Nucb2, which can be divided into two parts: the Zn2+-sensitive N-terminal half (consisting of nesfatin-1 and -2) and the Ca2+-sensitive C-terminal half (consisting of nesfatin-3). These results may also help to open a new discussion regarding the diverse roles that metal cations play in regulating the structure of Nucb2 and the various physiological functions of this protein.

Atomistic level characterisation of external surface species of mesoporous silica nanoparticles (MSN) poses a significant analytical challenge due to the inherently low content of grafted ligands. This study proposes the use of HR-MAS NMR spectroscopy for a molecular level characterisation of the external surface of carbohydrate-functionalised nanoparticles. MSN differing in size (32 nm, 106 nm, 220 nm) were synthesised using the sol-gel method. The synthesised materials displayed narrow particle size distribution (based on DLS and TEM results) and a hexagonal arrangement of the pores with a diameter of ca. 3 nm as investigated with PXRD and N2 physisorption. The surface of the obtained nanoparticles was functionalised with galactose and lactose using reductive amination as confirmed by FTIR and NMR techniques. The functionalisation of the particles surface did not alter the pore architecture, structure or morphology of the materials as confirmed with TEM imaging. HR-MAS NMR spectroscopy was used for the first time to investigate the structure of the functionalised MSN suspended in D2O. Furthermore, lactose was successfully attached to the silica without breaking the glycosidic bond. The results demonstrate that HR-MAS NMR can provide detailed structural information on the organic functionalities attached at the external surface of MSN within short experimental times.

An Annotated Bibliography of Published Works Concerning the Culture of Wilamowice and the Wymysorys Language, 2001–2020 This paper contains a list of 117 publications concerning the history, culture and language of Wilamowice, a small town in the south of Poland, populated by descendants of medieval colonists of Germanic origin. The town is well known for its unusual folk costume and the critically endangered minority language known as Wymysorys. Although the bibliography mainly covers academic works (monographs and journal articles), it also includes a supplement listing literary works published in Wymysorys. Each entry provides bibliographic information, keywords and a brief description of the publication. Additionally, links to online versions of the works are provided where possible. Bibliografia adnotowana publikacji dotyczących kultury Wilamowic i języka wilamowskiego z lat 2001–2020 Niniejsze opracowanie zawiera listę 117 publikacji dotyczących historii, kultury i języka Wilamowic – położonego na południu Polski miasta, zamieszkałego przez potomków średniowiecznych kolonistów germańskiego pochodzenia. Miejscowość ta słynie z niezwykle bogatego stroju ludowego i zagrożonego wymarciem języka mniejszościowego znanego jako wymysiöeryś. Bibliografia obejmuje przede wszystkim publikacje o naukowym charakterze (monografie i artykuły), ale zawiera również suplement wymieniający literaturę piękną wydawaną w języku wilamowskim. W każdej nocie zamieszczono opis bibliograficzny, słowa kluczowe i krótką prezentację zawartości publikacji. Dodatkowo, tam, gdzie było to możliwe, dołączone zostały odsyłacze do wersji online wymienionych prac.

The need for alternative strategies to fight bacteria is evident from the emergence of antimicrobial resistance. To that respect, photodynamic antimicrobial chemotherapy steadily rises in bacterial eradication by using light, a photosensitizer and oxygen, which generates reactive oxygen species that may kill bacteria. Herein, we report the encapsulation of 5,10,15,20-tetrakis(4-hydroxyphenyl)-21H,23H-porphyrin into acetylated lignin water-dispersible nanoparticles (THPP@AcLi), with characterization of those systems by standard spectroscopic and microscopic techniques. We observed that THPP@AcLi retained porphyrin’s photophysical/photochemical properties, including singlet oxygen generation and fluorescence. Besides, the nanoparticles demonstrated enhanced stability on storage and light bleaching. THPP@AcLi were evaluated as photosensitizers against two Gram-negative bacteria, Escherichia coli and Pseudomonas aeruginosa, and against three Gram-positive bacteria, Staphylococcus aureus, Staphylococcus epidermidis, and Enterococcus faecalis. THPP@AcLi were able to diminish Gram-positive bacterial survival to 0.1% when exposed to low white LED light doses (4.16 J/cm2), requiring concentrations below 5 μM. Nevertheless, the obtained nanoparticles were unable to diminish the survival of Gram-negative bacteria. Through transmission electron microscopy observations, we could demonstrate that nanoparticles did not penetrate inside the bacterial cell, exerting their destructive effect on the bacterial wall; also, a high affinity between acetylated lignin nanoparticles and bacteria was observed, leading to bacterial flocculation. Altogether, these findings allow to establish a photodynamic antimicrobial chemotherapy alternative that can be used effectively against Gram-positive topic infections using the widely available natural polymeric lignin as a drug carrier. Further research, aimed to inhibit the growth and survival of Gram-negative bacteria, is likely to enhance the wideness of acetylated lignin nanoparticle applications.

Magnetic domain structure of magnetic shape memory alloy was observed using backscattered electron detector in scanning electron microscope and using Fresnel imaging in transmission electron microscope. The sample subjected to additional ion polishing allowed observation of the contrast associated with the magnetic structure of the material under conditions that exclude the use of Foucault or Fresnel transmission electron microscopy imaging. The additional research conducted using atomic force microscopy showed a significant relationship between the method of preparation and the magnetic shape memory alloy sample surface. Keywords: Magnetic shape memory alloy, Magnetic domains, Ion polishing, CoNiGa, TEM

On a Certain Phonetic Feature of Wymysorys: An Analysis of Areal Aspects In Wymysorys, also known as Vilamovicean (a Germanic language spoken in Wilamowice, a small town in the south of Poland), velarized laterals [ɫ] have turned into [w]. This shift is characteristic of some Polish and German dialects, although in the latter it only occurs under certain conditions. Since Wymysorys displays a strong influence of Polish in many other respects, this change is more likely to have stemmed from contact with Polish. O pewnym szczególe z wilamowskiej fonetyki – próba analizy w kontekście arealnym W wilamowskim welaryzowane [ɫ] (kontynuant średnio-wysoko-niemieckiego l) przeszło w glajd [w]. Zmiana ta charakterystyczna jest dla różnych języków Europy, w tym dla polszczyzny i niektórych dialektów niemieckich (w tych ostatnich jednak zachodzi jedynie w pewnych warunkach). Silny wpływ polskiego na wilamowski (obserwowany nie tylko w fonetyce) uprawnia do stwierdzenia, iż omawiana zmiana jest wynikiem oddziaływania polszczyzny i dokonała się w ostatnim pokoleniu użytkowników wilamowszczyzny.

A simplified approach for rare earth elements leaching from NdFeB (neodymium-iron-boron) magnets was investigated. The possibility of simplifying the magnet recycling process by excluding grinding, milling and oxidative roasting unit operations was studied. Attempts to skip the demagnetization step were also conducted by using whole, non-demagnetized magnets in the leaching process. The presented experiments were conducted to optimize the operating conditions with respect to the leaching agent and its concentration, leaching time, leaching temperature and the form of the feed material. The use of hydrochloric and sulfuric acids as the leaching agents allowed selective leaching of NdFeB magnets to be achieved while leaving nickel, which is covering the magnets, in a solid state. The application of higher leaching temperatures (40 and 60 °C for sulfuric acid and 40 °C for hydrochloric acid) allowed us to shorten the leaching times. When using broken demagnetized magnets as the feed material, the resulting rare earth ion concentrations in the obtained solutions were significantly higher compared to using whole, non-demagnetized magnets.

Tissue engineering (TE) is a field of regenerative medicine that has been experiencing a special boom in recent years. Among various materials used as components of 3D scaffolds, naturally formed chitinous materials seem to be especially attractive because of their abundance, non-toxic and eco-friendly character. In this study, chitinous skeleton isolated from the marine sponge Aplysina fistularis (phylum: Porifera) was used for the first time as a support for the cultivation of murine fibroblasts (Balb/3T3), human dermal fibroblasts (NHDF), human keratinocyte (HaCaT), and human neuronal (SH-SY5Y) cells. Characterization techniques such as ATR FTIR, TGA, and μCT, clearly indicate that an interconnected macro-porous, thermostable, pure α-chitin scaffold was obtained after alkali–acid treatment of air-dried marine sponge. The biocompatibility of the naturally formed chitin scaffolds was confirmed by cell attachment and proliferation determined by various microscopic methods (e.g., SEM, TEM, digital microscopy) and specific staining. Our observations show that fibroblasts and keratinocytes form clusters on scaffolds that resemble a skin structure, including the occurrence of desmosomes in keratinocyte cells. The results obtained here suggest that the chitinous scaffold from the marine sponge A. fistularis is a promising biomaterial for future research about tissues regeneration.

In this paper, the study of surface modification of two-dimensional (2D), non-luminescent CdS nanoplates (NPLs) by thiol-containing ligands is presented. We show that a process of twophase transfers with appropriate ligand exchange transforms non-luminescent NPLs into spherical CdS nanoparticles (NPs) exhibiting a blue photoluminescence with exceptionally high quantum yield ~90%. In the process, transfer from inorganic solvent to water is performed, with appropriately selected ligand molecules and pH values (forward phase transfer), which produces NPs with modified size and shape. Then, in reverse phase transfer, NPs are transferred back to toluene due to surface modification by combined Cd (OL)2 and Cd (Ac)2. As a result, spherical NPs are formed (average diameter between 4 and 6 nm) with PL QY as high as 90%. This is unique for core only CdS NPs without inorganic shell.

Given a positive integer \(m\leq n/2\), Wojda conjectured in 1985 that if \(D_1\) and \(D_2\) are digraphs of order \(n\) such that \(|A(D_1)|\leq n-m\) and \(|A(D_2)|\leq 2n-\lfloor n/m\rfloor-1\) then \(D_1\) and \(D_2\) pack. The cases when \(m=1\) or \(m = n/2\) follow from known results. Here we prove the conjecture for \(m\geq\sqrt{8n}+418275\).

The virulence of bacterial outer membrane vesicles (OMVs) contributes to innate microbial defense. Limited data report their role in interspecies reactions. There are no data about the relevance of OMVs in bacterial-yeast communication. We hypothesized that model Moraxella catarrhalis OMVs may orchestrate the susceptibility of pathogenic bacteria and yeasts to cationic peptides (polymyxin B) and serum complement. Using growth kinetic curve and time-kill assay we found that OMVs protect Candida albicans against polymyxin B-dependent fungicidal action in combination with fluconazole. We showed that OMVs preserve the virulent filamentous phenotype of yeasts in the presence of both antifungal drugs. We demonstrated that bacteria including Haemophilus influenza, Acinetobacter baumannii, and Pseudomonas aeruginosa coincubated with OMVs are protected against membrane targeting agents. The high susceptibility of OMV-associated bacteria to polymyxin B excluded the direct way of protection, suggesting rather the fusion mechanisms. High-performance liquid chromatography-ultraviolet spectroscopy (HPLC-UV) and zeta-potential measurement revealed a high sequestration capacity (up to 95%) of OMVs against model cationic peptide accompanied by an increase in surface electrical charge. We presented the first experimental evidence that bacterial OMVs by sequestering of cationic peptides may protect pathogenic yeast against combined action of antifungal drugs. Our findings identify OMVs as important inter-kingdom players.

This article presents state-of-the-art welding methods and the weldability aspect of steels, particularly high-carbon nanobainitic (NB) steels, without carbide precipitates (CFB—carbide-free bainite). On the basis of research conducted to date, all welding methods with parameters and weld metals for NB CFB are presented. It was found that the process parameters significantly affected the mechanical properties of the welds, which were determined primarily by the properties of the low-temperature heat-affected zone. The microstructures of welded joints in the heat-affected and fusion zones are also described. The general requirements for welding processes, as well as problems and perspectives for further research, are presented.

Powłoki nanoszone metodą lutowania infiltracyjnego charakteryzują się wysoką odpornością na zużycie ścierne oraz dużą twardością. Z racji na wysoką komplikację nanoszenia powłok, postanowiono wykonać wstępne próby na drodze spiekania ziaren węglikowych z fazą ciekłą. Przeprowadzone badania miały na celu wstępne rozpoznanie różnic pomiędzy proszkami NiCrBSiFe a NiBSi w kontekście mikrostruktur i twardości otrzymanych kompozytów. Posłużyły one do zaplanowania koncepcji dalszej pracy badawczej. Projekt prowadzony był we współpracy z firmą AGRO// SELNET. Influence composition of mixtures NiCrBSiFe+WSC and NiBSi+WSC on their microstructure and hardness Abstract Infiltration brazed coatings are characterized by high wear resistance and high hardness. Because of the high complexity of coating process, it was decided to perform the initial samples by sintering the carbide grains with a liquid phase. The study aimed to initial recognition of the differences between NiCrBSiFe and NiBSi alloys in the context of the microstructure and hardness of the composites. These were used to plan the concept of further research. The project was performed in cooperation with AGRO//SELNET Company.

Objectives: The purpose of the research was to perform a stakeholder analysis for the Research and Development project of Mediprintic sp. z o.o. in order to confirm correctly identified parties for cooperation within the 1.1.2 PARP Start-up Platforms project. Methods: For the assessment of the selected stakeholders, the following tools were used: a tool to identify stakeholders and their interests, a tool to identify the importance and impact of stakeholders, a risk analysis for the undertaken activities of the project implementer with stakeholders together with the establishment of the necessary indicators to assess the achievement of the milestone. Results: From the research carried out, 14 key stakeholders for the success of the project were selected which are important for Mediprintic sp. z o.o. to be able to launch its product on the medical market. Conclussions: Completing a stakeholder analysis facilitates the decision-making process for management in order to prioritise the actions to be taken, taking into account the risks of cooperation with individual business partners.

Underwater wireless communication remains a challenging topic, particularly for applications such as wreck penetration where multipath and Doppler effects are very intense. These effects are becoming even more difficult to mitigate for fast data transmission systems that utilize wideband signals. Due to the low propagation speed of acoustic wave in the water, there is a significant difference between the Doppler shift for lower and upper frequencies of the utilized spectrum. To address these challenges, this paper describes various methods for determining the Doppler frequency shift for MFSK signals, including cross-correlation, double FFT, pilots, and additional Up-Down chirp signals. The reception quality of the transmitted data in a real environment was used as an evaluation criterion for each method. The tests were carried out in motion within the towing tank for different movement speeds of the transmitter relative to the receiver. The tank’s limited dimensions created conditions for multipath signal propagation. Under very difficult multipath signal propagation conditions, the pilots method was found to be the most effective. It gave over two times lower BER than the well-known Up-Down chirp method.

Versatile devices with tunable capabilities for controlling lasing wavelength and intensity are in high demand. Liquid crystals (LCs) exhibit immense potential for such applications, offering fine-tuning possibilities through external factors. On the other hand, laser technology is currently a research hotspot in optoelectronics, and also in practical applications. The recent market introduction of laser television marks a significant stride toward making such advanced technology accessible in every household. In synergy with laser pumping, the LCs unquestionably can be rediscovered. This study presents a comprehensive investigation into the crystallization phenomenon within a host-guest device, compact in size, free from moving parts, and integrating the liquid crystalline (LC) matrix doped with 3,4,9,10-tetra-(3-alcoxy-carbonyl)-perylene (THCP) dye. The focus lies in examining the influence of varying dye concentrations on multicolor fluorescence, lasing behavior, and device morphology. The systematic analysis of Random Lasing (RL) energy thresholds and the impact of DC voltage on light intensity modulation is demonstrated. Morphological changes were monitored in real-time using optical microscopy techniques, including crossed polarizer, and fluorescence imaging under 450 nm excitation. Utilizing advanced Transmission Electron Microscopy (TEM) techniques, we explore exceptional insights into our set of devices, providing novel information about the THCP crystallization process for the first time in the literature. To gain a comprehensive understanding of the crystal forming and molecular geometry we examined additionally the THCP dye, using X-ray diffraction and Raman spectroscopy. Furthermore, we showcase that varying the pumping energy enables multicolor tuning in the fabricated systems, presenting an attractive feature in the context of laser display technologies.