Additional Conditions Research Articles

Pattern formation from homogeneous states for an elliptic system with mixed interactions

In this paper, we are interested in the asymptotic behavior of a ground state vector solution for the following coupled nonlinear Schrödinger system { Δ u 1 − λ 1 u 1 + β 11 ( u 1 ) 3 + α β 12 u 1 ( u 2 ) 2 − β β 13 u 1 ( u 3 ) 2 = 0 Δ u 2 − λ 2 u 2 + α β 21 ( u 1 ) 2 u 2 + β 22 ( u 2 ) 3 − β β 23 u 2 ( u 3 ) 2 = 0 Δ u 3 − λ 3 u 3 − β β 31 ( u 1 ) 2 u 3 − β β 32 ( u 2 ) 2 u 3 + β 33 ( u 3 ) 3 = 0 in Ω and ∂ u i ∂ n = 0 on ∂Ω when α , β > 0 are very large. The existence of a ground state vector solution for (1) was proved in Byeon et al. [Pattern formation via mixed interactions for coupled Schrödinger equations under Neumann boundary condition. J Fixed Point Theory Appl. 2017;19:559–583] when α , β , α / β 2 − n 2 are large. We prove that if λ 3 is small, as α , β , α / β 2 − n 2 → ∞ , u 3 converges to a constant, u 1 and u 2 develop a small peak on ∂Ω . Under an additional condition α / β 2 − n 2 + δ → ∞ for some δ > 1 , we show that the peak point converges to a maximum point of the mean curvature of ∂Ω .

Selective Access to 2‐Phenylquinazolin‐4(3H)‐Ones and 2,3‐Dihydroquinazolin‐4(1H)‐Ones from Same Precursors in Organic Salts Derived DES

AbstractA binary mixture of organic salts, also known as ionic liquids, [C12mim][Br]:[MPIM][HCOO] denoted as BmIL1 has been explored as bifunctional catalyst for the selective synthesis of 2‐phenylquinazolin‐4(3H)‐ones and 2,3‐dihydroquinazolin‐(1H)‐ones from same precursors under metal, ligand and additive free conditions. The methodology has been extended to the synthesis of 2‐phenylquinazolin‐4(3H)‐ones via another pathway from different precursors under the same catalytic system. Greener synthesis of existing drugs reestablished the multifunctionality of BmIL1. Gram scale synthesis of both the products, DFT calculations and sc‐XRD data add significance to the developed protocol. Moreover, high atom economy and eco score values justify the sustainability of the methodology.

Classification of long-term disease patterns in inflammatory bowel disease and analysis of their associations with adverse health events.

With existing researches identifying an increased rate of long-term conditions (LTCs) among Inflammatory Bowel Disease (IBD) patients, yet there is a lack of exploration into the patterns of comorbidity and prognostic rates for IBD patients with multiple morbidities. The study included 8,305 participants who self-reported having IBD, comprising ulcerative colitis (UC) and Crohn's disease (CD). Latent class analysis (LCA) was utilized to create optimal categories of LTC combinations for UC and CD patients with additional long-term conditions. Using Cox proportional hazards models, we compared the all-cause mortality rates over a 16-year follow-up among UC and CD patients within different LTC categories, both without LTCs and with the addition of one LTC, the probability of major adverse cardiovascular events (MACE), and the rates of IBD-related surgeries. A total of 5,617 participants reported having two or more LTCs, with the LCA method identifying three prevalence categories among CD patients, and four prevalence categories among UC patients. The highest mortality rate among CD patients was found in category 3: (HR 1.789, 95% CI (1.439-2.224)), and the highest rates of MACE were also in category 3: (HR 11.432, 95% CI (9.332-14.005)), with hypertension being the distinguishing characteristic of this category, and the highest rates of IBD-related surgeries being associated with pain in category 1: (HR 1.217, 95% CI (0.983-1.506)). Among UC patients, the highest mortality rate was in category 3: (HR 2.221, 95% CI (1.837-2.684)), with the highest MACE rates found in category 3: (HR 6.422, 95% CI (5.659-7.288)), and the highest rates of IBD-related surgeries being associated with pain, also in category 3: (HR 1.218, 95% CI (1.041-1.425)). The rates of adverse health outcomes in IBD patients is closely associated with multimorbidity patterns, underscoring the need to fully consider multimorbidity patterns in the assessment, management, and treatment strategies for IBD.

Influence of rope fastening on the spectrum of its natural transverse vibrations

According to the previously developed method, which takes into account the bending stiffness of steel ropes during their transverse oscillation, the ropes of the pedestrian bridge ‘Lovers’ in the city of Tyumen were investigated. The obtained values of tension forces and bending stiffness were within the expected range. The high variation of bending stiffness values forced to pay attention to the accuracy of the initial values of rope lengths, which were obtained from the photograph. To measure the rope lengths, a method of nodal harmonic registration was proposed, but the results obtained by this method were higher than the values obtained from the photograph. The evaluation of measurement errors did not explain this overestimation, which led to the necessity to revise the solution of the differential equation of transverse oscillations. It turned out that previously only its partial solution was considered, assuming a hinged rope attachment, whereas it is cantilevered and has a bending reaction. Taking this feature into account by introducing an additional boundary condition allowed to improve the calculation model and explain the overestimation of the rope length in the method of nodal harmonics.Taking into account the nature of the rope attachment allowed us to introduce a generalised parameter s, which takes zero value for rigid cantilever attachment, and is equal to one for articulated attachment. Then the stiffness weakening inside the anchorage will be manifested by the growth of the parameter s and can be detected by the results of the oscillation spectrum registration.

Promises and challenges of genomic newborn screening (NBS) - lessons from public health NBS programs.

Newborn screening (NBS) in the United States began in the 1960s to detect inborn errors of metabolism that benefited from presymptomatic treatment compared with treatment after the development of symptoms and diagnosis. Over time, it expanded to include endocrinological disorders, hematological disorders, immunodeficiencies, and other treatable diseases such as lysosomal storage diseases (LSD), cystic fibrosis, X-linked adrenoleukodystrophy, and spinal muscular dystrophy. This expansion has been driven by new technologies (e.g., tandem mass spectrometry) and novel treatments (e.g., enzyme replacement therapy and stem cell transplant for LSDs). Advances in next-generation gene sequencing (NGS) enable rapid identification of many additional conditions that might benefit from early presymptomatic intervention. We review the NGS technologies that evolved as diagnostic testing and suggest issues to be resolved before their potential application to screening the asymptomatic population. We illustrate the importance of selecting diseases to be screened and propose recommendations to follow when variants of uncertain significance are found. We address ethical issues around achieving equity in the sensitivity of genomic NBS, access to follow-up and management, especially for people from diverse backgrounds, and other considerations. Finally, we discuss the potential benefits and harms of genomic NBS to the overall health of children with monogenic diseases. IMPACT: Genomic newborn screening programs are ongoing worldwide. Public discussion is needed as to whether genomic newborn screening should be offered as a public health program and, if so, what conditions should be screened for. Providers should understand that the sensitivity of genomic newborn screening is especially low for newborns from non-European populations. Methylation, large structural variants and repeat expansion variants are not amenable to next-generation sequencing-based genomic newborn screening. The article serves as a comprehensive guide to understanding issues that need to be solved before genomic newborn screening is implemented as a public health program.

Polish Speech and Text Emotion Recognition in a Multimodal Emotion Analysis System

Emotion recognition by social robots is a serious challenge because sometimes people also do not cope with it. It is important to use information about emotions from all possible sources: facial expression, speech, or reactions occurring in the body. Therefore, a multimodal emotion recognition system was introduced, which includes the indicated sources of information and deep learning algorithms for emotion recognition. An important part of this system includes the speech analysis module, which was decided to be divided into two tracks: speech and text. An additional condition is the target language of communication, Polish, for which the number of datasets and methods is very limited. The work shows that emotion recognition using a single source—text or speech—can lead to low accuracy of the recognized emotion. It was therefore decided to compare English and Polish datasets and the latest deep learning methods in speech emotion recognition using Mel spectrograms. The most accurate LSTM models were evaluated on the English set and the Polish nEMO set, demonstrating high efficiency of emotion recognition in the case of Polish data. The conducted research is a key element in the development of a decision-making algorithm for several emotion recognition modules in a multimodal system.

A mathematical model for wind-generated particle–fluid flow fields with an application to the helicopter cloud problem

We develop a model for the interaction of a fluid flowing above an otherwise static particle bed, with generally the particles being entrained or detrained into the fluid from the upper surface of the particle bed, and thereby forming a fully two phase fluidized cloud above the particle bed. The flow in this large-scale fluidized region is treated as a two-phase flow, whilst the key processes of entrainment and detrainment from the particle bed are treated by examining the local dynamical force balances on the particles in a thin transition layer at the interface between the fully fluidized region and the static particle bed. This detailed consideration leads to the formation of an additional macroscopic boundary condition at this interface, which closes the two-phase flow problem in the bulk fluidized region above. We then introduce an elementary model of the well-known helicopter brownout problem, and use the theory developed in the first part of the paper to fully analyse this model, both analytically and numerically.

Adults and Children Engage in Subtle and Fine-Grained Action Interpretation and Evaluation in Moral Dilemmas.

Understanding the actions of others is fundamental for human social life. It builds on a grasp of the subjective intentionality behind behavior: one action comprises different things simultaneously (e.g., moving their arm, turning on the light) but which of these constitute intentional actions, in contrast to merely foreseen side-effects (e.g., increasing the electricity bill), depends on the description under which the agent represents the acts. She may be acting intentionally only under the description "turning on the light," but did not turn on the light in order to increase the electricity bill. In preregistered studies (N = 620), we asked how adults and children engage in such complex subjective action interpretation and evaluation in moral dilemmas. To capture the deep structure of subjects' representations of the intentional structures of actions, we derived "act trees" from their response patterns to questions about the acts. Results suggest that people systematically distinguish between intended main and merely foreseen side-effects in their moral and intentionality judgments, even when main and side-effects were closely related and the latter were harmful. Additional experimental conditions suggest that, when given ambiguous information, the majority of subjects assume that agents act with beneficial main intentions. This "good intention prior" was so strong that participants attributed good intentions even when the harmful action was no longer necessary to resolve the dilemma (Study 2). These methods provide promising new ways to investigate in more subtle and fine-grained ways how reasoners parse, interpret, and evaluate complex actions.

Creep behavior of BFRP-confined coal gangue concrete under sulfate and high stress conditions

To recycle the coal gangue more economically and effectively, the basalt fiber reinforced polymer (BFRP) and coal gangue concrete (CGC) are combined to form a novel supporting structure in the underground mines, BFRP-confined CGC (FCGC). However, the underground mine environment is rich in sulfate corrosive ions, and meanwhile, the structure is subjected to a high sustained load. Thus, this paper presents an experimental and theoretical investigation on the long-term deformation properties of FCGC under sulfate and high stress conditions. The effects of inner concrete, FRP layer, stress-to-strength ratio, sulfate concentration and load duration time on the shrinkage and creep behavior were clarified in detail. The findings indicate that the shrinkage of FCGC is relatively lower as the BFRP confinement weakens the moisture exchange between inner CGC and external environment. In addition, under sulfate and high stress conditions, the creep strain and specific creep increase continuously in the early stage, while the growth rate gradually slows down in the later stage, where the high stress-to-strength ratio is the key factor. Moreover, when compared with a single high stress condition, the creep strain of FCGC is relatively larger under sulfate and high stress coupling conditions, attributed to the sulfate corrosion on the BFRP wraps. Theoretically, the ACI 209 was modified to predict the nonlinear creep of CGC, by introducing the coal gangue influence coefficient and the increasing coefficient of nonlinear creep. Furthermore, based on the creep model of CGC and BFRP, the nonlinear calculation model of FCGC was developed considering the creep of CGC under a triaxial-stress state and the interaction between inner CGC and BFRP confinement. Validations against the experimental results show that the nonlinear creep model of FCGC works well.

A Symmetric View of Fixed-Point Results in Non-Archimedean Generalized Neutrosophic Metric Spaces

In this paper, we extend prominent fixed-point theorems within the framework of symmetry, a structure increasingly relevant in decision-making, optimization, and uncertainty modeling. While previous studies have explored fixed-point theorems in non-Archimedean spaces, the influence of symmetry on the properties of mappings remains underexamined. To address this gap, we introduce and analyze the concepts of χ-contractions and χ-weak contractions, demonstrating how symmetry impacts the conditions for the existence of fixed points. Our methodology integrates these concepts in generalized neutrosophic metric spaces, providing a novel perspective on fixed-point theory. We perform a rigorous analysis, revealing new insights into their practical applications. However, our proposed system may face limitations in complex or dynamic environments, where additional conditions may be necessary to ensure the existence or uniqueness of fixed points.

Boronize Coatings Studied with a New Mass Transfer Model.

This study examined the development of Fe2B (diiron boronize) coatings on the surface of 35NiCrMo4 steel through the thermochemical surface hardening process called boronizing. The morphology and thickness of the boronize coatings were assessed using Scanning Electron Microscopy (SEM) and optical microscopy (OM). A novel mathematical mass transfer model was developed to estimate the diffusion coefficients of boron in hard coating. The presence of uniformly distributed boronize coatings with a typical sawtooth pattern on the surface of the substrate was confirmed. The boronize coating's chemical composition and phase constituents were analyzed utilizing X-ray energy dispersive spectroscopy (EDS) and X-ray diffraction analysis (XRD). The study confirmed the presence of a single-phase boronize coating (Fe2B). Furthermore, microhardness tests indicated that the boronized specimen's surface demonstrated an average hardness of approximately 1953 HV. The wear study were conducted using the pin-on-disk method under dry debonding conditions at room temperature to estimate the coefficient of friction (COF) of the boronized (average ≈ 0.35) and untreated (0.725) specimens. The results revealed approximately 200% improvement in wear resistance due to the boronized coating. The empirical validation of the mathematical model was carried out for two additional boronizing conditions at 1223 K for 3 h and 1273 K for 1.5 h, resulting in an estimated percentage error of around 2.5% for both conditions. Additionally, an ANOVA analysis was performed, taking into account the temperature and time factors. The findings indicate that both factors exert a substantial influence on the dependent variable (u), with temperature (T) contributing 64.68%, time (t) contributing 27.37%, and the interaction of both factors (T × t) contributing 5.13%.

Efficacy of Disinfectants for Monkeypox Virus Inactivation on High Touch Surface Materials in Low-Resource Settings.

Disinfection efficacy tests were conducted on surface carriers inoculated with the monkeypox virus (MPXV) by applying six disinfectant solutions (and three controls) on six surfaces common in low-resource settings: four nonporous surfaces (stainless steel, glass, plastic, and latex) and two porous surfaces (ceramic and wood). Disinfectants were wiped on carriers in triplicate, with a 1 min contact time: 0.05 and 0.5% sodium hypochlorite, 70% ethanol, two quaternary ammonium compound (QAC)-based disinfectants, and 1.4% hydrogen peroxide. MPXV was then quantified, and log10 removal values were calculated. Sodium hypochlorite (0.05 and 0.5%) and ethanol (70%) removed MPXV to below detection level, ≥ 99.97% reduction for nonporous surfaces, and ≥99.40% for wood, QAC-based disinfectants were efficacious on nonporous surfaces (≥99.97% inactivation) but had diminished efficacy on wood, a porous surface, and 1.4% H2O2 had limited efficacy across all tested surfaces. Results varied by disinfectant type and surface type. Based on our results, we recommend using 0.05% sodium hypochlorite or 70% ethanol with 1 min contact time to inactive MPXV on clean nonporous and porous surfaces. As MPXV is evolving, future research with additional disinfectants, application methods, and environmental conditions and research to understand adsorption, disinfection efficacy, and transmission risk on porous surfaces are needed to develop practical disinfection recommendations.

Identifying patterns in the structural-phase transformations when processing oxide doped waste with the use of carbon reducer

The object of this study is the structural and phase transformations during the carbon reduction of tungsten high-speed steel slag in order to obtain a resource-saving alloying additive. The problem is the loss of precious elements when obtaining and using alloying material from man-made raw materials. Solving the problem is related to the definition of technological parameters to enable the reduction of losses of the corresponding elements. As a result of increasing the degree of scale reduction from 33 % to 72 % and 85 %, the strengthening of the manifestation of the solid solution of carbon and alloying elements in α-Fe relative to FeWO4, FeO and Fe3O4 was revealed. Fe3C, WC, W2C, FeW3C, Fe3W3C, Fe6W6C, VC, V2C, Cr3C2, Cr7C3 and Cr23C6 also appeared. Along with this, rounded and multifaceted particles with different chemical composition and the formation of a spongy microstructure were found. It was established that the most acceptable degree of recovery is 85 %. But achieving a recovery rate of 72 % is also sufficient. This is explained by the fact that the residual carbon in the carbides provides an increased reducing capacity, which is realized during the further reduction of oxides in the liquid metal during alloying. The spongy microstructure results in faster dissolution in contrast to standard ferroalloys, which provides a reduction in melting time while reducing spent resources. No phases with an increased tendency to sublimation were found in the obtained alloying material. That is, no additional conditions are needed that restrain the loss of alloying elements during evaporation with a gaseous phase, which provides an increase in the degree of extraction of the corresponding elements. The properties of the resulting alloying material make it possible to use it in metallurgical production when smelting alloyed steel grades in an electric arc furnace, the composition of which does not have strict restrictions on the carbon content

Reliability design involving optimization with multiple objectives by means of probabilistic multi-objective optimization

AbstractAlthough there have been many achievements on single—objective models, the reliability research involving multi-objective optimization problems has not obtained satisfactory research results. In this paper, the reliability design involving optimization with multiple objectives is developed by means of probabilistic multi-objective optimization (PMOO), which considers the simultaneity of optimization of multiple objectives and treats both beneficial type of utility indexes and unbeneficial type of utility indexes of performance indicators equivalently and conformably. Three cases of reliability design concerning multi—objective optimization, i.e., reliability requirement as the additional constraint condition, reliability assessment as an additional optimized objective, and the mixture of these two cases, are formulated by means of PMOO, respectively. Furthermore, a typical example is given to show the procedure of the approach for reliability assessment involving multiple objectives by means of PMOO, which exhibits the validity of the present approach. The approach is objective without any subjective factors.

Organisation of medical care in large scale incidents: a practice-oriented research in Belgium

Abstract Background CBRNe incidents are emergency situations involving the release of chemical (C) or biological (B) substances or radiological/nuclear (RN) contamination, sometimes through an explosion (e). They can result from intentional malicious acts (e.g. terrorism) or unintentional situations (e.g. accidents). In this context, people (victims, care providers, witnesses), equipment (infrastructure, vehicles), animals, objects and/or the environment (buildings, ambulances) may be contaminated by a substance that could pose a threat to health. CBRNe incidents can quickly overwhelm the response capabilities of the affected region and put the healthcare system under great pressure. This research investigated ways of improving the organisation of medical care in CBRNe incidents in Belgium. Methods this study involved a mixed method approach in 2022-2023 with scoping and in-depth interviews with actors at operational and strategic levels (public health, Internal Affairs, army, fire departments), participative workshops with stakeholders, contextual desk search, ad hoc literature review and international comparison completed with interviews with national experts (Norway, The Netherlands, France and United Kingdom, United States of America). Results hospitals need to be distinguished in type 1 specialized hospitals for decontamination, major trauma management and advanced care for severely burned patients and in type 2 hospitals managing spontaneous arrivals of victims and non-specialised care. All hospitals need to have a strict lock-down policy. On the incident site, an emergency medical mobile team needs to manage the decontamination with the firefighters before the transfer to the most appropriate facility. Additional conditions were found to improve the efficiency of medical care. Conclusions this practice-oriented research contributes to a better organization of medical care in case of CBRNe incidents, with the emergence of practical and feasible solutions. Key messages • Hospitals need to be distinguished according to the need for specialised care in case of CBRNe incidents. • On site decontamination needs to be performed by health professionals and firefighters.

Self-Care of Older Patients Affected by at Least Two Chronic Conditions Between Heart Failure, Diabetes Mellitus and Chronic Obstructive Pulmonary Disease: A Comparative Study.

This study aims to describe disease-specific self-care behaviours in patients with heart failure (HF), diabetes mellitus (DM) and chronic obstructive pulmonary disease (COPD) in various combinations; to compare these self-care behaviours within patient groups; and to evaluate differences across these groups. Cross-sectional study. A total sample of 1079 older patients was recruited from outpatient clinics and home settings. Eligible patients were aged ≥ 65 years and had a diagnosis of HF and/or DM, and/or COPD, along with at least one additional chronic condition. Data were collected using validated tools: the Self-Care of Heart Failure Index, Self-Care of Diabetes Inventory and Self-Care of Chronic Obstructive Pulmonary Disease Inventory. Descriptive statistics were used to analyse disease-specific self-care behaviours. Group comparisons were performed using Student's t-test and univariate, followed by multivariate analyses of variance. The analysis focused on a subset of 223 patients who had a combination of at least two chronic conditions between HF, DM and/or COPD. The mean age of participants was 77.3 (SD 7.5) years, with a majority being female (53.4%). Self-care maintenance, monitoring and management for HF and COPD were found to be inadequate across all patient groups. Adequate self-care was only observed in DM management among those with HF and DM and in DM maintenance for those with DM and COPD treated with insulin. Significant differences in all self-care dimensions were observed across groups, particularly in patients managing all three conditions (HF, DM and COPD). The findings provide valuable insights into the complexities of self-care in patients with multiple chronic conditions, underscoring the need for tailored, integrated and patient-centred interventions. Healthcare strategies should focus on enhancing patient education and developing personalised approaches to improve health outcomes and quality of life in this population. All the authors have adhered to the EQUATOR guidelines STROBE Statement. A convenience sample of patients was recruited in outpatient clinics and their homes. Data were collected between March 2017 and August 2022, by face-to-face during routine outpatient visits or directly at the patient's home.

Do apologies promote the reintegration of former combatants? Lessons from a video experiment in Colombia

Transitional justice practices frequently involve public apologies where former combatants confess their wrongdoings and ask for forgiveness, with the underlying assumption that such displays facilitate the reintegration of ex-combatants into society. However, little is known about the public response to ex-combatant apologies. In this article, we investigate the causal effect of an armed group apology on attitudes toward ex-combatant reintegration in Colombia. Our study builds on a novel experiment implemented in Meta, a conflict-ridden department of Colombia. The experiment entailed exposing a subset of participants to a video in which a former rebel group leader apologizes for violent acts committed by their armed group during the civil war. To examine the extent to which external actors influence the effectiveness of apologies, we incorporated third-party ‘encouragements to forgive’ (endorsements) in two additional treatment conditions. Our analysis demonstrates that, on average, participants do not exhibit higher reintegration attitudes when exposed to the apology, regardless of third-party endorsements. However, the absence of a treatment effect is not due to an indifference to the apology. In an exploratory heterogeneity analysis, we show that the apology induces negative effects on some indicators of reintegration attitudes among participants that did not support the peace agreement. This finding aligns with qualitative data gathered in a follow-up survey, which indicates that opponents of the peace agreement generally describe negative emotional responses to the FARC-EP apology. The results call for a reconsideration of unchallenged prescriptions of public apologies after conflict.

Defining ethical criteria to guide the expanded use of Noninvasive Prenatal Screening (NIPS): Lessons about severity from preimplantation genetic testing.

We hypothesized that ethical criteria that guide the use of preimplantation genetic testing (PGT) could be used to inform policies about expanded use of non-invasive prenatal screening (NIPS). We used a systematic review of reasons approach to assess ethical criteria used to justify using (or not using) PGT for genetic conditions. Out of 1135 identified documents, we retained and analyzed 216 relevant documents. Results show a clear distinction in acceptability of PGT for medical vs. non-medical conditions. Criteria to decide on use of PGT for medical conditions are largely based on their severity, but there is no clear definition of "severity". Instead, characteristics of the condition that relate to severity are used as sub-criteria to assess severity. We found that characteristics that are used as sub-criteria for assessing severity include monogenic etiology, high penetrance, absence of treatment, early age of onset, shortened lifespan, and reduced quality of life. Consensus about the use of PGT is highest for conditions that meet most of these criteria. There is no consensus around the acceptability of using PGT to detect non-medical conditions. We propose that the same severity criteria could be used by policymakers to assess the acceptability of using other genetic tests in screening and practice, including for the use of NIPS for additional conditions as indications broaden.

Evaluation of the Effect of Growth Factors on Chlorophylls a and b Production from Microalgae.

Microalgae contain two main groups of pigments: chlorophylls and carotenoids. Chlorophyll is a green pigment that absorbs light energy and transforms it into chemical energy to facilitate the synthesis of organic compounds. This pigment serves as a valuable primary source for biotechnological input products in the food, pharmaceutical, and cosmetic industries due to its high antioxidant properties and coloring capabilities. The objective of this research was to evaluate the effect of growth factors (CO2 concentration, light color, and light intensity) through a Taguchi L4 experimental design on cell growth and the cellular content of chlorophyll a and b in Chlorella sorokiniana, followed by validation of the method using Haematococcus pluvialis microalgae as an additional study model. Cell growth was quantified using the optical density spectrophotometric technique at a wavelength of 550 nm. For the quantification of chlorophylls, a cell extract was obtained using a 90% pure acetone solution, and subsequently, the concentrations of chlorophylls a and b were quantified using spectrophotometric techniques at wavelengths of 647 nm and 664 nm, according to the method described by Jeffrey and Humphrey. The experimental results indicated that controlling conditions of low CO2 addition, purple light, and low light intensity increases both cell growth and the concentration of chlorophylls a and b within the cells. The implementation of this chlorophyll quantification method allows for quick, simple, and precise determination of chlorophyll content, as the wavelengths used are at the absorbance peaks of both types of chlorophylls, making this technique easily reproducible for any microalgae under study.

Zero-sum partitions of Abelian groups and their applications to magic- and antimagic-type labelings

The following problem has been known since the 80s. Let $\Gamma$ be an Abelian group of order $m$ (denoted $|\Gamma|=m$), and let $t$ and $\{m_i\}_{i=1}^{t}$, be positive integers such that $\sum_{i=1}^t m_i=m-1$. Determine when $\Gamma^*=\Gamma\setminus\{0\}$, the set of non-zero elements of $\Gamma$, can be partitioned into disjoint subsets $\{S_i\}_{i=1}^{t}$ such that $|S_i|=m_i$ and $\sum_{s\in S_i}s=0$ for every $1 \leq i \leq t$. Such a subset partition is called a \textit{zero-sum partition}. $|I(\Gamma)|\neq 1$, where $I(\Gamma)$ is the set of involutions in $\Gamma$, is a necessary condition for the existence of zero-sum partitions. In this paper, we show that the additional condition of $m_i\geq 4$ for every $1 \leq i \leq t$, is sufficient. Moreover, we present some applications of zero-sum partitions to magic- and antimagic-type labelings of graphs.