The modern material design aims to achieve multifunctionality by integrating structures in a diverse range, resulting in simple materials with embedded functions. Biological materials and organisms are typical examples of this concept, where complex functionalities are achieved through a limited material base. This review highlights the inspiration from multifunctional organisms and materials in nature, emphasizing their structural and functional integration. In particular, we discuss complex hierarchical architectures ranging from the nanoscale to the macroscale, to achieve multifunctional properties such as extreme pressure, impact and wear resistance, shape memory and self-healing, adhesiveness and anti-fouling, sensing-actuating and sensing-camouflage, and extreme environmental survival. These strategies of integrating structure and function are critical for promoting innovations and breakthroughs in the modern engineering materials and applications.

: Extra- and intra-cellular activity occurs under the direction of numerous inter-molecular interactions, and in any tissue or cell, molecules are densely packed, thus promoting those molecular interactions. Galectins and chemokines, the focus of this review, are small, protein effector molecules that mediate various cellular functions, in particular cell adhesion and migration, as well as cell signaling/activation. In the past, researchers have reported that combinations of these (and other) effector molecules act separately, yet sometimes in concert, but nevertheless physically apart and via their individual cell receptors. This view that each effector molecule functions independently of the other limits our thinking about functional versatility and cooperation, and, in turn, ignores the prospect of physiologically important inter-molecular interactions, especially when both molecules are present or co-expressed in the same cellular environment. This review is focused on such protein-protein interactions with chemokines and galectins, their homo- and hetero-oligomeric structures that they can form, and the functional consequences of those paired interactions.

In this study, literature on pore structure and chloride ion diffusivity was collected to investigate the correlation of pore structure indicators with diffusivity. Good correlation between total porosity and chloride ion diffusivity was found when the samples did not contain admixture materials and diffusion test was conducted without acceleration. Pore diameter indicators did not correlate with diffusivity. The diffusivity of cement paste was reduced by admixture materials compared to that without admixture materials even if the total porosity is the same. On the other hand, the diffusivity of concrete was not reduced by admixture materials.

Tree biomass and diversity relationship in mixed forest impacts on forest ecosystem services provisions. Tree biomass yield is driven by several aspects such as species identity, site condition, stand density, tree age as well as tree diversity expressed as species mingling and structural diversity. By comparing diverse degrees of tree mixture in natural forests we can insight on the ecosystem services provision level and dynamic. Two monitoring sites in the Castilian Northern Plateau (Spain) have been analyzed to disentangle the relationships between biodiversity levels and tree biomass yield. Two permanent one ha squared plots were established at Llano de San Marugan and Valdepoza. In each plot all individual trees were measured (diameter and height), georeferenced and its species identity defined. Tree species in the two sites were Pinus sylvestris, Pinus nigra, Pinus pinea, Quercus pyrenaica, Quercus ilex, Quercus faginea and Juniperus thurifera. From these datasets ten diversity indices that fall in three categories (species richness indices, species compositional/mingling indices and vertical structural indices) were used as predictor variables to fit several candidate models. By merging the trees by site (without considering the species identity) selected models include individual tree basal area as explanatory variable combining by addition or interaction with diversity indices. When species are analyzed independently structural diversity impacts on biomass yield in combination (additive or multiplicative) with tree size is negative Pinus nigra and positive for the other species.

This paper describes some neural representations that may be helpful for realising intelligence in the human brain. The ideas come from the author's own cognitive model, where a number of algorithms have been developed over time. Through developing and trying to implement the architecture, ideas like separating the data from the function have become architecturally appropriate and there have been several opportunities to make the system more orthogonal. Similarly for the human brain, neural structures may work in-sync with the neural functions, or may be slightly separate from them. Each section discusses one of the neural assemblies with a potential functional result, that cover ideas such as timing or scheduling, inherent intelligence and neural binding. Another aspect of self-representation or expression is interesting and may help the brain to realise higher-level functionality based on these lower-level processes.

(-)-Zeylenone is a promising cytotoxic agent，which is a natural product isolated from Uvaria grandiflora Roxb. Though substantial antitumor mechanism has been researched , little has focused on its enantiomer (+)-Zeylenone.This article will try to find a gram scale synthesis method of (+)-Zeylenone and explain the structure-activity relationship of this kind of compound. Total synthesis of (+)-zeylenone was completed in 13 steps with quinic acid as starting material in 8.8% overall yield. The highlight of the route was the control of the three carbon’s chirality by clever use of single step dihydroxylation under the direction of the key C-3 chirality. In addition, zeylenone derivatives were designed and synthesized and their antitumor activity were evaluated against three human cancer cell lines using the CCK8 assay. Structure-activity relationship suggested compounds with both two absolute configurations exhibited good activity. Besides, hydroxyls at C-1/2 position were crucial for the activity and esterification of C-1 hydroxyl with large groups made the activity disappeared. Hydroxyl at C-3 position was also important as proper ester substituent could increase the potency.

To understand the relationship between water permeability and the pore structure of cementitious materials, literature that studied both water permeability and the pore structure are reviewed, and their correlation is studied. Although the majority of this data is for cement paste, mortar, concrete, and cemented soil are also included. Based on this study, it is established the determination coefficient between water permeability and the total pore volume is very low; however, those between water permeability and the critical, threshold, and median pore diameters, respectively, are moderate. On the other hand, the threshold pore diameter, derived based on the percolation theory, exhibits a very high determination coefficient. The calculated water permeability, using the Katz and Thompson equation, agrees with the reported water permeability quantitatively to a certain level, but is overestimated.

Changes in the atomic and electronic structure of silicon carbide 3C-SiC (β-SiC), resulting from lead adsorption, have been studied within the density functional theory. The tests were conducted for three representative surfaces with varying degrees of lead coverage. Results indicate that chemisorption occurs, with the strongest binding, found on the hexagonal surface (111) in interaction with three dangling bonds. The adsorption energy rises with increasing coverage, especially as the surface approaches saturation. Analysis of the data was focused on parameters important for corrosion processes such as bond distances, binding energies, Bader charges and charge density difference.

Background Some patients with mild cognitive impairment (MCI) experience gait disturbances. However, there are few reports on the relationship between gait disturbance and cognitive function in patients with MCI. Therefore, we investigated the neural correlates of gait characteristics related to cognitive dysfunction. Methods Eighty patients diagnosed with MCI from three dementia centres in Gangwon-do, Korea were recruited for this study. We defined MCI as a Clinical Dementia Rating global score of 0.5 or higher, with a memory domain score of 0.5 or greater. The patients were classified as having either early or late MCI based on their Mini Mental Status Examination z-scores. Multiple logistic regression analysis was performed to examine the association between the gait characteristics and cognitive impairment. Analyses included variables such as age, sex, years of education, number of comorbidities, body mass index and height. Results Gait velocity, step count, step length, heel-to-heel base support, swing and stance phase duration, and support time were associated with cognitive function. A decrease in gray matter volume in the right pericalcarine area was associated with gait characteristics related to cognitive dysfunction. An increase in the curvature of gray matter in the right entorhinal, right lateral orbitofrontal, right cuneus, and right and left pars opercularis areas was also associated with gait characteristics related to cognitive dysfunction. Conclusion Since gait impairment is an important factor in determining activities of daily living in patients with mild cognitive impairment, the evaluation of gait and cognitive functions in patients with mild cognitive impairment is important.

Optical properties of the cornea are responsible for correct vision, ultrastructure allows optical transparency and biomechanical properties governs the shape, elasticity or stiffness of the cor-nea affecting ocular integrity and intraocular pressure. Therefore, optical aberrations, corneal transparency, structure and biomechanics play a fundamental role in the optical quality of hu-man vision, ocular health and refractive surgery outcomes. However, the convergence of those properties is not yet reported at macroscopic scale within the hierarchical structure of the cornea. This work explores the relationships between biomechanics, structure and optical properties (corneal aberrations and optical density) at macrostructural level of the cornea through dual Placido-Scheimpflug imaging and air-puff tonometry systems in a healthy young adult popula-tion. Results showed convergence between optical transparency, corneal macrostructure and biomechanics.

Antimicrobial resistance is an increasing problem for the global public health. One of the strategies to combat this issue is the synthesis of novel antimicrobials through rational drug design based on extensive structure-activity relationship studies. The thiazole nucleus is a prominent feature in the structure of many authorized antimicrobials, being clubbed with different heterocycles. The purpose of this review is to study the structure-activity relationship in antimicrobial thiazoles clubbed with various heterocycles reported in the literature between 2017 and 2022, in order to offer an overview of the last years in terms of antimicrobial research and provide a helpful instrument for future research in the field.

In patients with schizophrenia, metabolic syndrome is associated with cognitive impairments. We carried out a second analysis of data from a longitudinal trial to examine the relationship between weight gain and cognitive function in patients with first-episode schizophrenia (FES) over the first 6-month antipsychotic treatment. Baseline and 6-month endpoint measurements were taken for both cognitive function and body weight. Linear and logistic regression analyses were applied to investigate the bidirectional relationship between weight gain and cognitive function. Clinically relevant weight gain (CRW) was defined as an increase in body weight ex-ceeding 7%. The final analysis included 337 participants. Lower baseline scores in processing speed (OR=0.837, p=0.007), working memory and attention (OR=0.889, p=0.043), and executive function (OR=0.863, p=0.006) domains were significantly associated with CRW at the 6-month endpoint. After adjusting for confounders, CRW was found to be associated with improvement in the Brief Visuospatial Memory Test (p=0.036). The findings suggest that patients with lower baseline cognitive performance experienced more substantial weight gain. Conversely, weight gain was correlated with cognitive improvements, particularly in the domain of visual learning and memory. This suggested a potential bidirectional relationship between weight gain and cog-nitive function in patients with first-episode schizophrenia.

Arrestin-1, or visual arrestin, exhibits an exquisite selectivity for light-activated phosphorylated rhodopsin (P-Rh*) over its other functional forms. That selectivity is believed to be mediated by two well-established structural elements in the arrestin-1 molecule, the activation sensor detecting the active conformation of rhodopsin and the phosphorylation sensor responsive to the rhodopsin phosphorylation, which only active phosphorylated rhodopsin can engage simultaneously. However, in the crystal structure of the arrestin-1-rhodopsin complex there are arrestin-1 residues located close to rhodopsin, which do not belong to either sensor. Here we tested by site-directed mutagenesis the functional role of these residues in wild type arrestin-1 using direct binding assay to P-Rh* and light-activated unphosphorylated rhodopsin (Rh*). We found that many mutations either enhanced the binding only to Rh* or increased the binding to Rh* much more than to P-Rh*. The data suggest that the native residues in these positions act as binding suppressors, specifically inhibiting the arrestin-1 binding to Rh* and thereby increasing arrestin-1 selectivity for P-Rh*. This calls for the modification of a widely accepted model of the arrestin-receptor interactions.

The altimeter-derived ocean currents have been sparsely evaluated against in situ measurements in the Arctic, particularly for extended time periods. This study uses the extensive mooring array situated in the Fram Strait, representing one of the longest ocean current records, to investigate the relationship between in situ and satellite-derived currents in the region. The primary objective of this research is to analyze the vertical structure of the West Spitsbergen Current (WSC), its spatio-temporal coherence, and its association with surface geostrophic currents during the period of 1997-2012. To assess the vertical structure of the WSC, we utilized the Empirical Orthogonal Functions (EOF) and cross-correlation analysis between neighboring moorings. Remarkably, both velocity components exhibited robust vertical coherence, particularly within the waters of the North Atlantic Inflow, at depths exceeding 800 m. These findings underscore the potential for surface measurements to effectively complement data gaps and facilitate the reconstruction of deeper currents with a monthly temporal resolution. Notably, the surface measurements explain approximately 67% of the variance in the top 800 m of the water column.This comprehensive investigation advances our understanding of the West Spitsbergen Current and its vertical characteristics in the Arctic. Moreover, our findings highlight the valuable synergy between in situ and satellite-derived data, providing critical insights for future ocean current studies in this ecologically sensitive region.

Fish processing by-products such as frames, trimmings, and viscera of commercial fish species are rich in proteins. Thus, they have the potential to be an economical source of proteins that may be used to obtain bioactive peptides and functional protein hydrolysates for the food and nutraceutical industries. The structure, composition, and biological activities of peptides and hydrolysates depend on the freshness and the actual composition of the material. Peptides isolated from fisheries by-products showed antioxidant activity. Changes of hydrolysis parameters changed the sequence and properties of the peptides, and determined their physiological functions. Optimization of the value of such peptides and the production costs must be considered for each particular source of marine by-products and for their specific food applications. This review will discuss the functional properties of fisheries by-products prepared using hydrolysis and their potential food applications. It also reviews the structure-activity relationships of the antioxidant activity of peptides as well as challenges to the use of fisheries by-products for protein hydrolysates production.

HspA1A, a molecular chaperone, translocates to the plasma membrane (PM) of stressed and cancer cells. This translocation results in HspA1A’s cell-surface presentation, which renders tumors radiation insensitive. To specifically inhibit the lipid-driven HspA1A’s PM translocation and devise new therapeutics it is imperative to characterize the unknown HspA1A’s lipid-binding regions and determine the relationship between the chaperone and lipid-binding functions. To elucidate this relationship, we determined the effect of phosphatidylserine (PS)-binding on the secondary structure and chaperone functions of HspA1A. Circular dichroism revealed that binding to PS resulted in minimal modification on HspA1A’s secondary structure. Measuring the release of inorganic phosphate revealed that PS-binding had no effect on HspA1A’s ATPase activity. In contrast, PS-binding showed subtle but consistent increases in HspA1A’s refolding activities. Furthermore, using a Lysine-71-Arginine mutation (K71A; a null-ATPase mutant) of HspA1A we show that although K71A binds to PS with affinities similar to the WT, the kinetics of the binding are significantly different, probably because of the mutant’s inability to achieve specific conformations. These observations suggest a two-step binding model that includes conformational changes and strongly support the notion that the chaperone and lipid-binding activities of HspA1A are dependent but the regions mediating these functions do not overlap. These findings provide the basis for future interventions to inhibit HspA1A’s PM-translocation in tumor cells, making them sensitive to radiation therapy.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

The genetic diversity of local coffee populations is crucial to breed new varieties better adapted to the increasingly stressful environment due to climate change and the evolving consumer preferences. Unfortunately, local coffee germplasm conservation and genetic assessment have not received much attention. Molecular tools offer substantial benefits in identifying and selecting new cultivars or clones suitable for sustainable commercial utilization. New annotation methods, such as chloroplast barcoding, are necessary to produce accurate and high-quality phylogenetic analyses. This study used DNA barcoding techniques to examine the genetic relationships among fifty-six accessions collected from the southern part of Saudi Arabia. PCR amplification and sequence characterization were used to investigate the effectiveness of four barcoding loci, namely atpB-rbcl, TrnL-TrnF, TrnT-TrnL, and TrnL. The maximum nucleotide sites, nucleotide diversity, and an average number of nucleotide differences were recorded for atpB-rbcl, while TrnT-TrnL had the highest variable polymorphic sites, segregating sites, and haploid diversity. Among the four barcode loci, TrnT-TrnL recorded the highest singleton variable sites, while TrnL recorded the highest parsimony information sites. Furthermore, the phylogenetic analysis clustered the Coffea arabica genotypes into four different groups, with three genotypes (KSA31, KSA38, and KSA46) found to be the most divergent genotypes standing alone in the cluster and remained apart during the analysis. The study demonstrates the presence of considerable diversity among coffee populations in Saudi Arabia. Furthermore, it also shows that DNA barcoding is an effective technique for identifying local coffee genotypes, with potential applications in coffee conservation and breeding efforts.

The aminoglycoside 6′-N-acetyltransferase type Ib [AAC(6′)-Ib] is a common cause of resistance to amikacin and other aminoglycosides in Gram-negatives. Utilization of mixture-based combinatorial libraries and application of the positional scanning strategy identified an inhibitor of AAC(6′)-Ib. This inhibitor’s chemical structure consists of a pyrrolidine pentamine scaffold substituted at four locations (R1, R3, R4, and R5). The substituents are two S-phenyl (R1 and R4), an S-hydroxymethyl (R3), and a 3-phenylbutyl (R5) groups. Another location, R2, does not have a substitution, but it is named because its stereochemistry was modified in some compounds utilized in this study. Structure-activity relationship (SAR) analysis using derivatives with different functionalities, modified stereochemistry, and truncations were carried out by assessing the effect of the addition of each compound at 8 µM to 16 µg/ml amikacin-containing media and performing checkerboard assays varying the concentrations of the inhibitor analogs and the antibiotic. The results showed that: 1) the aromatic functionalities at R1 and R4 are essential, but the stereochemistry is essential only at R4, 2) the stereochemical conformation at R2 is critical, 3) the hydroxyl moiety at R3 as well as stereoconformation are required for full inhibitory activity, 4) the phenyl functionality at R5 is not essential and can be replaced by aliphatic groups, 5) the location of the phenyl group on the butyl carbon chain at R5 is not essential, 6) the length of the aliphatic chain at R5 is not critical, 7) all truncations of the scaffold resulted in inactive compounds. Molecular docking revealed that all compounds preferentially bind to the kanamycin C binding cavity, and binding affinity correlates with the experimental data for most of the compounds evaluated. The SAR results in this study will serve as the basis for the design of new analogs in an effort to improve their ability to induce phenotypic conversion to susceptibility in amikacin-resistant pathogens.

A novel series of thiazole based-1,3,4-thiadiazoles were designed and prepared via the reaction of the 2-(4-methyl-2-phenylthiazole-5-carbonyl)-N-phenylhydrazinecarbothioamide with the appropriate hydrazonoyl chlorides. The structures of the newly synthesized compounds were established based on spectroscopic evidences and their alternative syntheses. Thirteen new 1,3,4-thiadiazoles have been evaluated for their anticancer activity against liver carcinoma cell line (HepG2). Also, their structure activity relationship (SAR) was studied. The 1,3,4-thiadiazoles 12d, 12c, 6g,18b, 6c, and 6f(IC₅₀ = 0.82, 0.91, 1.06, 1.25, 1.29 and 1.88 µM, respectively) have promising antitumor activity against liver carcinoma cell line (HepG2).

This study utilized panel data from 31 Chinese provinces over a period of nine years to investigate the impact of green finance on the upgrading of the agricultural industrial structure. A fixed-effect model was employed, and the findings indicate that green financing has a positive effect on the growth of China's agricultural industry. However, regional disparities exist, particularly in the uneven distribution of green financing across the eastern, central, and western regions. Moreover, it emphasizes the need to consider regional differences and tailor development strategies accordingly. To promote further development and transformation of China's agricultural industrial structure, the study recommends innovative green financial products, improved regulations and policies, and the integration of digital technologies.

Chronic kidney disease patients treated by hemodialysis present a high cardio-vascular morbidity and mortality. There is an imperative need for novel biomarkers in identifying and to offer possible therapeutically intervention in these patients. We performed a prospective observational cohort study on 77 patients in the period October 2021 – October 2023. We measured serum plasma levels of Interleukin 1-Beta, Galectin 3, human suppression of tumorigenicity factor 2, bone morphogenetic protein 2 and fibroblastic growth factor 23 at the inclusion. We evaluated the correlations of these biomarkers with cardiac function and structure evaluated by echocardiography. Mean age was 61.02 (±11.81) years, 45 (56.2%) males and with a dialysis vintage of 4.95 (2.4-7.8) years. Median ejection fraction was 51 (43-54 %) and more than two thirds of the patients presented valvular calcifications. Overall mortality was 22%. Interleukin 1-Beta correlated positively with ejection fraction and global longitudinal strain and negatively with left atrium diameter and left ventricle tele systolic diameter. Galectin 3 values negatively correlated with aortic valve fibrosis and mitral valve calcifications and human suppression tumorigenity factor 2 negatively correlated with mitral valve calcifications. Some of these novel biomarkers could be used to better asses the cardio-vascular disease in patients on maintenance hemodialysis.

Repurposing previously approved drugs may fast track the route to clinic for potential senotherapeutics and improves the inefficiency of the clinical drug development pipeline. We carried out a repurposing screen of 240 clinically approved molecules in human primary dermal fibroblasts for effects on CDKN2A expression. Molecules demonstrating effects on CDKN2A expression underwent secondary screening for senescence-associated beta galactosidase (SAB) activity, based on effect size, direction and/or molecule identity. Selected molecules then underwent a more detailed assessment of senescence phenotypes including proliferation, apoptosis, DNA damage, senescence-associated secretory phenotype (SASP) expression and regulators of alternative splicing. A selection of the molecules demonstrating effects on senescence were then used in a new bioinformatic structure-function screen to identify common structural motifs. 90 molecules displayed altered CDKN2A expression at one or other dose, of which 15 also displayed effects on SAB positivity in primary human dermal fibroblasts. Of these, three were associated with increased SAB activity, and 11 with reduced activity. The female synthetic sex hormones; diethylstilboestrol, ethynyl estradiol and levonorgestrel; were all associated with a reduction in aspects of the senescence phenotype in male cells, with no effects visible in female cells. Finally, we identified that the 30 compounds that decreased CDKN2A activity the most had a common substructure linked to this function. Our results suggest that several drugs licenced for other indications may warrant exploration as future senotherapies, but that different donors and potentially different sexes may respond differently to senotherapeutic compounds. This underlines the importance of consideration of donor-related characteristics when designing drug screening platforms.

Structure–function relationships in proteins have been one of the crucial scientific topics. Heme proteins have diverse and pivotal biological functions. Therefore, clarifying their structure–function correlation is significant to understand their functional mechanism and is informative for various fields of science. In this study, we constructed convolutional neural network models for predicting protein functions from the tertiary structures of heme-binding sites (active sites) of heme proteins to examine the structure–function correlation. As a result, we succeeded in the classification of oxygen-binding protein (OB), oxidoreductase (OR), proteins with both functions (OB–OR), and electron transport protein (ET) with high accuracy. Although the misclassification rate for OR and ET was high, the rates between OB and ET and between OB and OR were almost zero, indicating that the prediction model works well between protein groups with very different functions. However, predicting the function of proteins modified with amino acid mutation(s) remains a challenge. Our findings indicate a structure–function correlation in the active site of heme proteins. This study is expected to be applied to the prediction of more detailed protein functions such as catalytic reactions.

Advances in next-generation sequencing have facilitated the discovery of a multitude of long non-coding RNAs (lncRNAs) with pleiotropic functions in cellular processes, disease and viral pathogenesis. It came as no surprise when viruses were also revealed to transcribe their own lncRNAs. Among them, gammaherpesviruses, one of the three subfamilies of the Herpesviridae, code their largest number. These structurally and functionally intricate non-coding (nc) transcripts modulate cellular and viral gene expression to maintain viral latency or prompt lytic reactivation. The lncRNAs allow the virus to escape cytosolic surveillance, sequester and re-localize essential cellular factors and modulate the cell cycle and proliferation. Some viral lncRNAs act as “messenger molecules”, transferring information about viral infection to neighboring cells. This broad range of lncRNA functions is achieved through lncRNA structure-mediated interactions with effector molecules of viral and host origin, including other RNAs, proteins and DNAs. In this review, we discuss examples of gammaherpesvirus-encoded lncRNAs, emphasize their unique structural attributes, and link them to viral life cycle, pathogenesis and disease progression. We will address their potential as novel targets for drug discovery and propose future directions to explore lncRNA structure and function relationship.

Background: Targeting Hepatitis B virus (HBV) infection in human is crucial due to its adverse. Herbal medicine has long been significant in this regard, with flavonoids demonstrating promising results. Hence, establishing a way of identifying flavonoids with anti-HBV activities is the aim of the present study. Methods: Flavonoid structures with anti-HBV activities were retrieved. A flavonol-based pharmacophore model was established using LigandScout v4.4. Screening was performed using the PharmIt server. A QSAR equation was developed and validated with independent sets of compounds. Applicability domain (AD) was defined using Euclidean distance calculations for model validation. Results: The best model, consisting of 57 features was generated. HTS using the flavonol-based model resulted in 509 unique hits. The model's sensitivity and specificity were 71% and 100%, respectively. The QSAR model with two predictors, x4a and qed, exhibited strong predictive performance with an adjusted-R² value of 0.85 and 0.90 of Q2. Conclusion: The QSAR model has been validated with two separate chemical sets, guaranteeing the model's reproducibility and usefulness for other flavonols by utilizing the predictive characteristics of X4A and qed. These results provide new possibilities for discovering future anti-HBV drugs by integrating modeling and experimental research.

Background: In schizophrenia (SZ), social cognition mediates the relationship between neurocognition and social functioning. Although people with major depressive disorder (MDD) also exhibit cognitive impairments, which are often prolonged, little is known about the role of social cognition in MDD. Methods: Using data obtained through an internet survey, 210 patients with SZ or MDD were selected using propensity score matching based on their demographic information and illness duration. Social cognition, neurocognition, and social functioning were evaluated using the Self-Assessment of Social Cognition Impairments, Perceived Deficits Questionnaire, and Social Functioning Scale, respectively. The mediation effects of social cognition on the relationship between neurocognition and social functioning were examined in each disease group. Invariances of the mediation model across the two groups were then analyzed. Results: The SZ and MDD groups had mean ages of 44.49 and 45.35 years, contained 42.0% and 42.8% women, and had mean illness durations of 10.76 and 10.45 years, respectively. In both groups, social cognition had significant mediation effects. Configural, measurement, and structural invariances across the groups were established. Conclusion: The role of social cognition in patients with chronic depression was similar to that in schizophrenia. Social cognition could be a common endophenotype for various psychiatric disorders.

This paper investigates the impact of debt financing on dividend payments when they face the agency costs of free cash flow. Focusing on a sample of 120 firms listed on the Saudi Stock Exchange during the period 2011-2021. The study found a negative association between agency cost of free cash flow and dividend payment. More importantly, our research highlights the significant role of long-term debt in making more prudent use of free cash flow. The obligation to meet interest and principal payments acts as an incentive for them to steer clear of unprofitable expenses and risky investments. Concurrently, long-term debt imposes restrictive clauses in debt contracts, such as minimum dividend distribution requirements, which further encourage higher dividend payments. Since interest and debt repayments are fixed obligations, using free cash flow for dividend disbursement is considered a more profitable and beneficial approach for shareholders in the context of Saudi Arabia.

Modern forestry systems are based upon typologies of forest types (FT). Many proposals were developed in Argentina, but without following unified criteria. The objective was to compare different approaches based on (i) functional forests (phenoclusters), and (ii) forest canopy-cover composition by tree species. We employed data of National Forest Inventories, forest models and climate data, comparing the proposals using univariate analyses. We test the performance of phenoclusters to differentiate the variability of native forests (proxy: forest structure), biodiversity (proxy: indicator species) and environment (proxies: soil carbon stock, elevation, climate). We proposed a simple forest type classification methodology based on species composition, considering basal area of tree species. Finally, we compared the performance of both proposals. In regions where monospecific forests are predominant, the classifications based on forest canopy-cover composition are feasible, but phenoclusters allowing to increase the complexity at landscape level. In those regions were predominant multi-specific stands, the classifications based on forest canopy-cover composition are useless, and phenoclusters allowing to decrease the complexity at landscape level. These results allowing to harmonize national FT classifications by using criteria and indicators to achieve sustainable forest management and conservation proposals.

Whether there is any inclination between structures and functions of antimicrobial peptides (AMPs) is a mystery yet to be unraveled. AMPs have various structures associated with many different antimicrobial functions, including antibacterial, anticancer, antifungal, antiparasitic and antiviral activities. However, none has yet reported any antimicrobial functional tendency within a specific category of protein/peptide structures nor any structural tendency of a specific antimicrobial function with respect to AMPs. Here we examine the relationships between structures categorized by three structural classification methods (CATH, SCOP and TM) and seven antimicrobial functions with respect to AMPs using an enrichment analysis. The results show that antifungal activities of AMPs were tightly related to two-layer sandwich structure of CATH, knottin fold of SCOP, and the first structural cluster of TM. The associations with knottin and TM cluster 1 even sustained through the AMPs with a low sequence identity. Besides, another significant mutual enrichment was observed between the third cluster of TM and anti-gram-positive-bacterial/anti-gram-negative-bacterial activities. The findings of the structure-function inclination further our understanding of AMPs and could help us design or discover new therapeutic potential AMPs.

Due to its devastating consequences, late life depression is an important public health problem. The aim of the study was the analysis of variables which may potentially influence risk of depression (GDS-SF). Furthermore, the aim was to study possible mediating effect of given variables on the relationship between the total protein concentration and risk of depression in older-adults with chronic diseases, and physical function impairment. The research sample included a total of 132 older adults with chronic conditions and physical function impairments, remaining under a long-term care in residential environment. Negative linear correlation was observed between patients’ physical functionality, total protein concentration, concentration of HDL cholesterol, arm circumference, and the risk of depression. Considerably stronger relationship was observed between total protein concentration, and GDS-SF, in elderly suffering from sensory dysfunction (b = −6.42, 95% CI = −11.27; −1.58). The effect of the mediation between depression risk is correlated to total protein concentration in blood serum, and the mediators are probably low function impairment and low levels of 25 (OH)D vitamin. Cohort control research is suggested to confirm the hypothesis.

The motivation for investigating the issues presented in this article stemmed from a need to understand better the relationship in long-established physics formulas and extract the information they provided using conventional methods. Based on the definition of magnetic flux quantization, which is based on a combination of fundamental physical constants, the Planck constant, and the particle’s elementary charge, this work explores the results that arise when this equation is combined with the equation of the Bohr-level electrostatic force acting on the electron, which leads to a new mathematical relationship between the combined expressions. The new relationship yields novel theoretical findings related to the known universal constants. Following this insight, the formalism developed in this paper indicates that the mass of the electron and other subatomic particles is associated with the magnitude of the square of the magnetic flux quantum, which makes up the particle. This conclusion is not as strange as it may seem, as the square of the magnetic flux quantum appears in the context of magnetic energy in a current loop and, according to Einstein’s special theory of relativity, energy is equivalent to mass. Another aspect described at the end of this paper demonstrates the connection between the square of the magnetic flux quantum through the Bohr radius and the significance of the wave function in the atom. The theoretical results are in full accordance with experimental results published by NIST CODATA 2018 that I’ve used, which validates the existence of the relationship.

Plasminogen (Plg) is the inactive form of plasmin (Plm) that exists in two major glycoforms, referred to as glycoforms I and II (GI and GII). In the circulation, Plg assumes an activation-resistant 'closed' conformation via interdomain interactions and is mediated by the lysine binding site (LBS) on the kringle (KR) domains. These inter-domain interactions can be readily disrupted when Plg binds to lysine/arginine residues on protein targets or free L-lysine and analogues. This causes Plg to convert into an 'open' form which is crucial for activation by host activators. In this study, we investigated how various ligands affect the kinetics of Plg conformational change using small-angle X-ray scattering (SAXS). We began by examining the open and closed conformations of Plg using size-exclusion chromatography (SEC) coupled with SAXS. Next, we developed a high throughput (HTP) 96-well SAXS assay setup. This method enables us to determine the Kopen value, which is used to compare ligands’ effect on Plg conformation directly. Based on our analysis using Plg GII, we have found that the Kopen for ε-aminocaproic acid (EACA) is approximately three times greater than that of Tranexamic acid (TXA), which is widely recognized as a highly effective ligand. We demonstrated further that Plg undergoes a conformational change when it binds to the C-terminal peptides of the inhibitor α2-antiplasmin and receptor Plg‑RKT. Our findings suggest that, besides the C-terminal lysine, internal lysine(s) are also necessary for the formation of open Plg. Finally, we compared the conformational changes of Plg GI and GII directly and found that the closed form of GI, which has an N-linked glycosylation, is less stable. To summarize, we have successfully determined the response of Plg to various ligand/receptor peptides by directly measuring the kinetics of its conformational changes.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

A series of water diversion projects to address the uneven distribution of water resources in China involve the construction of a large number of hydraulic tunnels. As the lining structure that maintains the stability and durability of the tunnels, it is prone to durability damage during the operation process, which in turn affects the water transmission safety and water supply capacity. Therefore, it is important to evaluate the durability of hydraulic tunnel lining structure. Considering the randomness and fuzziness of the factors affecting the durability of hydraulic tunnel lining structure, this paper proposes a comprehensive evaluation model based on the coupling of set-pair analysis and extension. The G1 method and the simple correlation function method are used to determine the subjective and objective weights of the evaluation indexes respectively, and the combination weight is assigned based on the principle of minimum entropy; the set-pair analysis principle is used to establish the linkage affiliation function, calculate the comprehensive linkage affiliation of the object to be evaluated, and the maximum affiliation principle is used to judge the durability level of the hydraulic tunnel lining structure. Finally, taking a section of hydraulic tunnel as an example, the model proposed in this paper is used to calculate its durability grade as Class III, with the set-pair potential SHI(H) = 7.5856, which is consistent with the actual engineering practice, and a comparative study is done in combination with the AHP-Extenics method. It is verified that the evaluation model can scientifically and reasonably evaluate the durability of hydraulic tunnel lining structure, providing a basis for subsequent maintenance and reinforcement.

A new strategy to nanoengineer gold/fluorocarbon multilayer (ML) nanostructures is reported. We have investigated the morphological changes occuring at the metal-polymer interface in multilayer structures with varying volume fraction of gold (Au) and the kinetic growth aspect of the microscale properties of nano-sized Au in plasma polymer fluorocarbon (PPFC). Investigations were carried out at various temperatures and annealing time by means of grazing incidence small-angle and wide-angle X-ray scattering (GISAXS and GIWAXS). We have fabricated a series of multilayers with variying volume fraction (0.12, 0.27, 0.38) of Au and bilayer periodicity in ML structure. They show an interesting granular structure consisting of nearly spherical shaped nanoparticles within the polymer layer. The nanoparticle (NP) morphology changes due to the collective effects of NPs diffusion within ensembles in the in-plane vicinity and inter-layer with increasing temperature. The in-plane NPs size distinctly increases (from 1.9 to 4 nm) with increasing temperature. The NPs become more spherical thus reducing the surface energy. Linear growth of NPs with temperature and time shows diffusion-controled growth of NPs in the ML structure. The structural stability of the multilayer is controlled by the volume ratio of the metal in polymer. At room temperature UV-Vis shows a blueshift of the plasmon peak from 560 nm in ML Au/PTFE_1 to 437 nm in Au/PTFE_3. We have identified the fabrication and post-deposition annealing conditions to limit the Local Surface Plasmon resonance (LSPR) shift (from 〖∆λ〗_LSPR=180 nm (Au/PTFE_1) to 〖∆λ〗_LSPR=67 nm (Au/PTFE_3 ML)) and their optical response over a wide visible wavelength range. A variation in the dielectric constant of the polymer in precence of varying Au inclusion is found to be the main factor affecting the LSPR frequency. Our finding may provide insights in Nano engineering ML structure can be useful to systematically control the growth of NPs in polymer matrix.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

In this work we develop a new algorithm for efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where number of the grid-points is dependent on the input parameter $y$. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation especially at smaller range of the parameter x.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Intrinsic disorder accounts for the flexibility of protein loops, molecular building blocks that are largely responsible for the processes and molecular functions of the living world. While loops likely represent early structural forms that served as intermediates in the emergence of protein structural domains, their origin and evolution remains poorly understood. Here, we conduct a phylogenomic survey of disorder in loop prototypes sourced from the ArchDB classification. Tracing prototypes associated with protein fold families along an evolutionary chronology revealed ancient prototypes tended to be more disordered than their derived counterparts, with ordered prototypes developing later in evolution. This highlights the central evolutionary role of disorder and flexibility. While mean disorder increased with time, a minority of ordered prototypes exist that emerged early in evolutionary history, possibly driven by the need to preserve specific molecular functions. We also revealed percolation of evolutionary constraints from higher to lower levels of organization. Percolation resulted in trade-offs between flexibility and rigidity that impacted prototype structure and geometry. Our findings provide a deep evolutionary view of the link between structure, disorder, flexibility and function, as well as insights into the evolutionary role of intrinsic disorder in loops and their contribution to protein structure and function.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.

It is well known that the primes and prime powers have a deep relationship with the nontrivial zeros of Riemann’s zeta function. This is a reciprocal relationship. The zeros and the primes are encoded in each other and are reciprocally recoverable. Riemann’s zeta is an extended or continued version of Euler’s zeta function which in turn equates with Euler’s product formula over the primes. This paper shows that the zeros of the converging Dirichlet or Catalan beta function, which requires no continuation to be valid in the critical strip, can be easily determined. The imaginary parts of these zeros have a deep and reciprocal relationship with the odd primes and odd prime powers. This relationship separates the odd primes into those having either 1 or 3 as a remainder after division by 4. The vector pathway of the beta function is such that the real part of its zeros has to be a half.

Course-based Undergraduate Research Experiences (CUREs) in high-enrollment, introductory classes are a 37 potentially transformative approach to retaining more students in STEM majors. We developed and piloted a CURE 38 in the introductory biology courses at the University of Washington. This CURE focuses on analyzing experimental 39 evolution of antibiotic resistance in Escherichia coli and generates data on two topics relevant to clinical practice: 40 compensatory mutations and cross-drug effects. By studying mutations in central cellular machinery that confer drug 41 resistance, students not only gain insight into fundamental cellular phenomena, but also recognize the molecular 42 basis of a medically important form of evolutionary change, connecting genetics, microbiology, and evolution.

We introduce new metric structures on a smooth manifold (called “weak" structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures (φ,ξ,η,g) and allow us to take a fresh look at the classical theory and find new applications. This assertion is illustrated by generalizing several well-known results. It is proved that any Sasakian structure is rigid, i.e., our weak Sasakian structure is homothetically equivalent to a Sasakian structure. It is shown that a weak almost contact structure with parallel tensor φ is a weak cosymplectic structure and an example of such a structure on the product of manifolds is given. Conditions are found under which a vector field is a weak contact vector field.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Proof of the Riemann hypothesis is obtained using the properties of the Gamma function, the Bernoulli function, and limitations imposed by the rational relations of the complex roots of the Riemann zeta function, and the rational relations of the complex Gamma functions.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

CoO-ZnO-based composites have attracted considerable attention for the development of energy storage devices because of their multifunctional characterization and ease of integration with existing components. This paper reports the synthesis of CoO@ZnO (CZ) nanostructures on Ni foam by the CBD method for facile and eco-friendly supercapacitor applications. The formation of a CoO@ZnO electrode functioned with cobalt, zinc, nickel and oxygen groups was confirmed by X-ray diffraction, X-ray photoelectron spectroscopy, low and high-resolution of scanning electron microscopy, and transmission electron microscopy. The as-synthesized hierarchical nanocorn skeleton-like structure of CoO@ZnO-3h (CZ3h) electrode delivered a higher specific capacitance of 1136 F/g at a current density of 3 A/g with outstanding cycling stability, showing 98.3% capacitance retention over 3000 cycles in an aqueous 2 M KOH electrolyte solution. This retention was significantly better than that of other prepared electrodes, such as CoO (CO), ZnO (ZO), CoO@ZnO-1h (CZ1h), and CoO@ZnO-7h (CZ7h) (274, 383, 240 and 537 F/g, respectively). This superior capacitance was attributed to the ideal surface morphology of CZ3h, which is responsible for the rapid electron/ion transfer between the electrolyte and electrode surface area. The enhanced features of the CZ3h electrode highlight potential applications in high performance supercapacitors, solar cells, photocatalysis, and electrocatalysis.

Abstract: Background: Restless Legs Syndrome /Willis-Ekbom disease (RLS/WED) has occasionally -but not consistently- been associated with cognitive, and most notably, language and executive impairment. The present study was conducted to investigate the cognitive trajectories of older individuals with RLS/WED. Methods: Participants were drawn from the randomly selected, older (>64 years), population-based HELIAD cohort. Individuals without dementia, with available neuropsychological evaluations at baseline and follow-up were considered for potential eligibility. A comprehensive assessment examining five principal components of cognition (memory, visuo-spatial ability, attention, executive function, and language) was administered to the partici-pants. Generalized estimating equations analysis was used to examine the unadjusted and adjusted (for critical factors and covariates) effects of RLS/WED on cognition over time. Results: A total of 1003 predominantly female, older (72.9 ±4.9 years) partici-pants, with follow-up evaluations after a mean of 3.09 ±0.85 years and without demen-tia at baseline and follow-up were included in the present study. Among them, 81 were diagnosed with RLS/WED at baseline. Global cognition, memory, attention, executive and visuo-perceptual skills did not differ between those with and without RLS/WED. However, the RLS/WED group performed worse on language at baseline by 0.249 of a standard deviation, while demonstrating a mitigated language decline over time, by 0.063 of a standard deviation. The unadjusted models yielded similar results. Conclu-sions: Our findings were indicative of a baseline language disadvantage among older individuals with RLS/WED, but the initial discrepancy tends to dissolve over time.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

Crystal structures of simple metals and binary alloy phases based on the face-centered cubic (fcc) structure are analyzed within the model of Fermi sphere – Brillouin zone interactions to understand the stability of original cubic structure and derivative structures with distortions, superlattices and vacancies. Examination of the Brillouin-Jones configuration in relation to the nearly-free electron Fermi sphere for several representative phases reveals significance of the electron energy contribution to the phase stability. Representation of complex structures in the reciprocal space clarifies their relationship to the basic cubic cell.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

Many studies discuss carbon-based materials because of the versatility of its element. They include different opinions for scientific problems and discuss fairly at convincing and compelling levels within the scope and application. A gas-state carbon atom converts into various states depending on its conditions of processing. The electron transfer mechanism in the gas-state carbon atom is responsible to convert it into various states, namely, graphite, nanotube, fullerene, diamond, lonsdaleite and graphene. The shape of ‘energy trajectory’ enables transferring electrons from the left- and right-sides of an atom is like a parabola. That ‘energy trajectory’ is linked to states (filled state and suitable nearby unfilled state) where force-exertion along the poles of transferring electrons is remained balance. So, the mechanism of originating different states of a gas-state carbon atom is under the involvement of energy first. This is not the case for atoms executing confined inter-state electron-dynamics as the force is involved first. Graphite-, nanotube- and fullerene-state atoms ‘partially evolve partially develop’ (form) their structures. These possess one-dimensional, two-dimensional and four-dimensional ordering of atoms, respectively. Their structural formation also comprises ‘energy curve’ having a shape-like parabola. Transferring suitable filled state electron to suitable nearby unfilled state is under a balance force exerting along the poles. The graphite structure under only attained-dynamics of atoms can also be formed but in two-dimension. Here, binding energy between graphite-state carbon atoms is for a small difference of exerting forces along their opposite poles. Structural formation in diamond, lonsdaleite and graphene atoms involve energy to gain required infinitesimal displacements of electrons through which they maintain orientationally-controlled exerting forces along dedicated poles. In this study, the growth of diamond is found to be south to east-west (ground) where atoms bound ground to south. Thus, diamond atoms merge for a tetra-electron ground to south topological structure. Lonsdaleite atoms merge for a bi-electron ground to just-south topological structure. The growth of graphene is found to be north to ground where atoms bound ground to north. Thus, graphene atoms merge for a tetra-electron ground to north topological structure. Glassy carbon exhibits layered-topological structure where, tri-layers of gas-, graphite- and lonsdaleite-state atoms successively bind in repetitive order. Nanoscale hardness is also sketched based on different force-energy behaviors of different state carbon atoms. Here, structure evolution in each carbon state atom explores its own science.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Population is the main driver of land systems and environmental change. However, the population is usually treated as a variable that only considers the population number, and the multidimensional population structure is largely ignored. There has been a systematic transition of population structure in the past several decades, such as the changing household structure, the increasing aging population and divorce rate, and human migration. All these have direct or indirect impacts on land use and environmental issues. Here, we will take China as an example to examine the relationship between household dynamics and land use change in China by exam-ining changes in household structure and land use change in China between 1980 and 2020. The results show:1) the number of households increased by 130.95% from 1980 to 2020, while the population only increased by 42.83%. The size of households decreased from 4.41 to 2.92 in China from 1982 to 2020. The household dynamics vary from province to province, which is affected by urbanization rate and economic development. 2) Birth rates, divorce rates, population aging, and migration all affect household structure, which directly or indirectly affects changes in land use systems. 3) The changes in China's land use are interlinked and interact with changes in household structure, evident in the increase in residential land use and the abandonment of arable land. The rising household number increased the area of urban and rural settlement, leading to the fragmentation of cultivated land and the reduction of ecological land. To regulate land use change for sustainable development, future land use planning should take into effect of household dynamics, and reduce the negative effects of household dynamics on land systems and environmental change.

Most non-infectious diseases are associated with dysfunction of proteins or protein complexes. Аssociation between sequence and structure is analyzed since a long time, and analysis of sequence organization in domains and motifs is actual research area. A mathematical method is proposed here to identify the hierarchical organization of protein sequences. The method is based on pentapeptide as a unit of protein sequences. This method was applied on a non-homologous dataset of protein sequences. The analysis revealed 11 hierarchical levels of protein sequence organization, showing the relationship of these multiple fragments of sequences. Using different examples, we illustrated how the fragments of the spatial structure of protein correspond to the elements of the hierarchical structure of the protein sequence. A hierarchical structure is observed in the protein sequence. This methodology is an interesting basis for mathematically based classification of elements of spatial organization of proteins. Elements of the hierarchical structure of different levels of the hierarchy can be used for biotechnological and medical problems.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

Background: Upper extremities’ function impairments (UEFI) and gait impairment are frequently reported even in the early stages of Multiple Sclerosis (MS) disease. These motor deficits can negatively affect the quality of life (QOL) in MS patient. Exercise has been repeatedly introduced as a beneficial adjuvant therapy for MS, attenuating a wide range of physical and psychological symptoms without any side effects or increased risks of relapse or exacerbation in disease symptoms.Aim: This paper investigates the effect of multi-function swing suspension training (MFSST) program on upper and lower extremities’ function (ULEF), and QOL in MS women according to expanded disability status scale (EDSS) score.Design: Experimental method with a pre-test and post-test design with control group. Setting: The department of Sports Injuries and Corrective Exercise at the Shahid Bahonar University of Kerman.Population: Forty-seven MS women.Methods: Eligible subjects who matched the selection criteria were randomly assigned into three groups as follow: i. Intervention group A (EDSS of 2 – 4), ii. Intervention group B (EDSS of 4.5 – 6.5), and iii. Control group (EDSS of 2 – 6.5). The intervention groups have been trained by the SET program for a duration of 8 weeks. At baseline and after the intervention, the upper extremities’ function (UEF) and the lower extremities’ function (LEF) were assessed by 9-hole peg test (9HPT) and the timed 25-foot walk (T25FW) test, respectively. Moreover, participants’ QOL was measured using the Short Form questionnaire (SF-36).Results: A significant difference was found between the pre-test and post-test variables of walking speed and upper extremity endurance in intervention groups, and between the intervention groups and control group (P < 0.05). Compared to control group, both intervention groups showed improvements in all subscales of QOL, except emotional role limitation score.Conclusions: In summary, these results show that the present protocol of MFSST could be effective in improving ULEF and QOL in MS patients, showing the improvements after 4^th week. Moreover, this protocol was more useful for patients with an EDSS score of more than 4.5. Therefore, it seems that exercise therapy should be considered as a beneficial clinical intervention approach to improve ULEF and QOL in MS patients.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

Dry eye syndrome (DES) has become increasingly prevalent due to the prolonged use of digital devices in modern society. Individual supplementation with lutein or docosahexaenoic acid (DHA) demonstrated potential benefits for eye health. This study aimed to investigate the effects of lutein plus DHA complex supplementation on DES, visual function, and memory in healthy individuals. Thirty-four participants, aged 40~60 years, received lutein/DHA complex supplements (containing 10 mg free-form lutein, 200 mg DHA, 30 mg red algae extract (astaxanthin), phosphatidylserine, and vitamin A) for 12 weeks. Ophthalmological examinations and memory tests were carried out, and a questionnaire was administered at weeks 0, 6, and 12 of the study. After 12 weeks of the intervention, the tear break-up time had significantly increased, and intraocular pressure (IOP) had significantly decreased. This suggests that lutein/DHA complex supplementation may reduce the IOP and offer potential benefits for DES, as indicated by improved tear stability.

This work uses a new approach to investigate the Riemann hypothesis, drawing conclusions about its trueness. It is based on the more general method presented in a very recent publication, by the same author, showing in detail how to approach that very well-known and interesting problem. This is achieved by means of the theory of dynamical systems (Poincaré index associated to equilibria of 2-dimensional systems) and the study of the zeros of the Dirichlet eta function, defined by a Dirichlet series. By using the well-known fact that the zeros of the eta function include all zeros of the Riemann zeta function in the (open) critical strip, excluded the critical line, ((0,1/2) ∪ (1/2,1)) × (−∞,∞), the development proceeds using only the eta function. In addition, the open and simply connected region (1/2,1) × (0,∞) is used along the text, taking into account the symmetries of zeros of the functions under analysis in the critical strip. The basic line of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the eta function, assuming the existence of a zero of the eta function outside the critical line (in (1/2,1) × (0,∞)), and investigating the resulting unfoldings. Eventually, an inconsistency occurs and the proof ends by contradiction.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

The Marchenko method is a data-driven way which makes it possible to calculate Green's functions from virtual points in the subsurface by the reflection data at the surface, only requiring a macro velocity model. This method requires collocated sources and receivers. However, in practice, subsampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green's functions. To solve this problem, this paper proposes to integrate sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply sparse inversion during the iterative process. Our work not only reduces the strict requirements on acquisition geometries, but also avoids the complexity and instability of direct inversion for Marchenko equations. This new method is applied to a two-dimensional numerical example with irregular sampled data. The result shows that it can effectively fill gaps of the obtained focusing functions and Green's functions in the Marchenko method.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modelling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to find the sums over inverse powers of zeroes for the incomplete Gamma- and Riemann zeta- functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeroes of the Hurwitz zeta-function , including the sum over the inverse first power of its appropriately defined non-trivial zeroes. We also study some related properties of the Hurwitz zeta-function zeroes. In particular, we show that for any natural N and small real epsilon, when z tends to n=0, -1, -2… we can find at least N zeroes of zeta in the - vicinity of 0 for sufficiently small epsilon, as well as one simple zero tending to 1, etc.

Micro satellites must survive severe mechanical conditions during their launch phase. Therefore, structural design requirements are imposed on the micro satellites. These requirements are the strength requirement and the stiffness requirement. Usually, the structural design of a micro satellite is performed using the internal stress analysis and the natural frequency analysis, which are based on a Finite Element Method (FEM). The validity of this structural design is evaluated through vibration tests. In an early stage of development, which has a FEM model of a satellite in the process of creation, presumption of the natural frequency of a satellite may be difficult. In this study, a simple method for determining the longitudinal and lateral minimum natural frequencies of the micro satellites during the ascent phase was clarified. The structure of the micro satellites used in this research is made of aluminum alloy, and they have a monocoque structure. The Young's modulus and moment of inertia of area used to calculate the minimum natural frequencies were determined using the area ratio of the monocoque structure to the entire satellite. When this method is used, the estimated minimum natural frequencies of the longitudinal direction and the lateral direction are in agreement with the measured values acquired by the vibration tests. In order to shorten the process of micro satellites development, this paper describes a practical estimation method of the minimum natural frequency for micro satellites.

The crystal structure of Pb₁₀(PO₄)₆O, the proposed matrix for the potential room-temperature superconductor LK-99, Pb_10-xCu_x(PO₄)₆O (x = 0.9-1.0), has been reinvestigated by single-crystal X-ray diffraction using crystals prepared by Merker and Wondratschek (The crystal structure is trigonal, P, a = 9.8109(6), c = 14.8403(12) Å, V = 1237.06(15), R₁ = 0.0413 using 3456 unique observed reflections. The crystal structure of Pb₁₀(PO₄)₆O is a superstructure with regard to the ‘standard’ P6₃/m apatite structure type. The doubling of the c parameter is induced by the ordering of ‘additional’ O’ atoms within the structure channels running parallel to the c axis and centered at (00z). The O’ atoms form short bonds to the Pb1 atoms, resulting in splitting the Pb1 site into two, Pb1A and Pb1B. The structural distortions are further transmitted to the Pb phosphate framework formed by four Pb2 sites and PO₄ groups. The structure data previously reported by Krivovichev and Burns (Z. Kristallogr. 2003, 218, 357-365) may either correspond to the Pb₁₀(PO₄)₆O_x(OH)_2-x (x ~ 0.4) member of the Pb₁₀(PO₄)₆O - Pb₁₀(PO₄)₆(OH)₂ solid solution series, or to the high-temperature polymorph of Pb₁₀(PO₄)₆O (with the phase with doubled c parameter being the low-temperature polymorph).

Nickel nitrate diammine, Ni(NH₃)₂(NO₃)₂, can be synthesised from the thermal decomposition of the nickel nitrate hexammine, Ni[(NH₃)₆](NO₃)₂. The hexammine decomposes in 2 distinct steps; the first releases 4 equivalents of ammonia while the second involves the release of NO_x, N₂ and H₂O to yield NiO. The intermediate diammine compound can be isolated following the first deammoniation step or synthesised as a single phase from the hexammine under vacuum. Powder X-ray diffraction (PXD) experiments have allowed the structure of Ni(NH₃)₂(NO₃)₂ to be solved for the first time. The compound crystallises in orthorhombic space group Pca2₁ (a = 11.0628 (5) Å, b = 6.0454 (3) Å, c = 9.3526 (4) Å; Z = 4) and contains 11 non-hydrogen atoms in the asymmetric unit. Fourier Transform Infrared (FTIR) spectroscopy demonstrates that the bonding in the ammine is consistent with the structure determined by PXD.

A monocular vision pose estimation and identification algorithm used on a small spacecraft for future orbital servicing is studied in this paper. A tracker spacecraft equipped with a short-range vision system is proposed to recover the 3D structural model of a space target in orbit and automatically identify its solar panels and main body using only visual information from an onboard camera. The proposed reconstruction and identification framework is tested using structure-from-motion and point cloud identification methods. The Efficient Perspective-n-Points (EPnP) descriptor is used for pose estimation. Triangulated points are used for component segmentation by means of orientation histogram descriptors. Experimental results based on laboratory images of a spacecraft model show the effectiveness and robustness of our approach.