The invariants of the binary decimic

We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants

The invariants of the binary nonic

We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets of degrees

SL2-modules of small homological dimension

Let Vn be the SL2-module of binary forms of degree n and let V = Vn1+...+Vnp . We consider the algebra R of polynomial functions on V invariant under the action of SL2. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hdR. Popov gave in 1983 a classification of the cases in which hdR <=10 for a single binary form (p = 1) or hdR 1). We extend Popov's result and determine for p = 1 the cases with hdR 1 those with hdR <= 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R

Prevalence of comorbidities and survival analysis of COVID-19 patients – an observational study from a tertiary healthcare center in North West Romania

Objectives. The experience accumulated in the last two years shows that the prevention of COVID-19 in people with comorbidities (protective measures, vaccination, etc.) still remains a public health priority. In this context, the aim of our study was to perform a retrospective, observational study in order to assess the time-to-death and risk factors of mortality among COVID-19 patients. Materials and Methods. The study was conducted on 177 patients admitted to Oradea Emergency County Hospital, Bihor, Romania, between October and December 2021. Inclusion criteria were patients over 18 years positive for COVID-19 in upper respiratory tract samples using real-time PCR test. Exclusion criteria were pregnant women, ageyears, and patients with incomplete records at admission. Results. The mortality rate was assessed in correlation with the most prevalent comorbidities such as diabetes, cardiovascular diseases, hypertension, chronic kidney disease, and chronic pulmonary diseases, either alone or associated. During hospitalization, an aggravated health condition was noticed for 71 patients (40.11%). Among them, 47 patients were transferred to the intensive care unit (66.20%) due to severe respiratory failure, aggravation of associated diabetes and/or other associated comorbidities. Ventilation support was necessary in 122 cases (68.63%). The average survival time was 8.66 days. In conclusion, we found that the most prevalent comorbidities were cardiovascular diseases, being the major risk factor for mortality or aggravation after hospitalization. Its association with diabetes caused a risk of death 2.1 times higher than in patients without comorbidities. Based on Kaplan–Meier survival analysis, we found that the in-hospital survival rate was significantly higher in females compared to males (50.52% vs 33.75%)

The effects of SGLT2 inhibitors in patients with metabolic dysfunction-associated fatty liver disease; a narrative review

Worldwide, metabolic dysfunction-associated fatty liver disease (MAFLD) is a significant public health concern, especially since more than fifty percent of people with type 2 diabetes are affected by it. This pathological condition includes all states of fatty liver disease, from non-alcoholic fatty liver disease (NAFLD) to steatohepatitis (NASH). Prolonged evolutions can lead to cirrhosis and cancer, so treatment must be started early. Hepatic steatosis may be improved by sodium glucose co-transporter 2 inhibitors (SGLT2 inhibitors), which prevent glucose reabsorption in the proximal renal tubule and increase urinary excretion, thus lowering plasma glucose levels. Experimental studies in animal models have suggested that SGLT2 inhibitors may have beneficial modulatory effects on NAFLD and NASH, while numerous clinical trials have demonstrated their favorable effects on the liver enzymes, body mass index, blood lipids, blood glucose, and insulin resistance in NAFLD patients. This review highlights the state of knowledge regarding the epidemiology, diagnosis and pathogenetic pathways of MAFLD, focusing primarily on the effectiveness of SGLT2 inhibitors as a promising drug class in the treatment of NAFLD

Influența exercitată de Led-uri și tuburile fluorescente, de diferite culori, asupra proceselor regenerative și a morfogenezei la culturile in vitro de Rebutia heliosa

The paper traces how the light source and light color influence the regenerative processes and morphogenesis in vitro cultures of Rebutia heliosa. To establish the vitroculture of R. heliosa, some explants from young plants, either buds or rounds cut from young stems and cross-sectioned were considered. The culture medium consisted of: macroelements and Fe EDTA Murashige-Skoog (1962), microelements Heller (1953), a mineral mixture to which the following vitamins were added: pyridoxine HCl, thiamine HCl and nicotinic acid (each 1 mg/l, each), m-inositol – 100 mg/l, sucrose – 20 g/l and agar-agar 7 g/l, without growth phytoregulators.The variable element was the lighting source. Fluorescent tubes and LEDs (monochrome but differently coloured) have been used: blue (λ = 470 nm), yellow (λ = 580 nm), green (λ = 540 nm), red (λ = 670 nm) as well as LED`s emitting white light (λ = 510 nm) at a luminous intensity of 1000 lux. The evolution of R. heliosa vitro cultures was monitored for 90 days and analyzed their reaction variability. Based on the comparative study, the following can be stated: the light of fluorescent tubes is more suitable for the morphogenesis of R. heliosa vitroplants, but the processes of regeneration and organogenesis are directly influenced by the source and color of light influenced, thus rhizogenesis and caulogenesis is favored by the presence of green and red light emitted by LEDs, while the white and yellow light of fluorescent tubes favors the caulogenesis and callusogenesis processes.Lucrarea urmărește modul în care sursa de iluminare și culoarea luminii influențează procesele regenerative și morfogeneza în vitroculturile de R. heliosa. Pentru a înființa vitrocultura de R. heliosa am prelevat explante de la plante t inere, fie mugurași, fie rondele decupate din tulpinile tinere și secţionate transversal. Mediul de cultură utilizat de noi a constat din: macroe-lemente şi Fe EDTA Murashige-Skoog (1962), microelemente Heller (1953), amestec mineral la care au fost adăugate vitaminele: piridoxină HCl, tiamină HCl şi acid nicotinic (câte 1 mg/l, fiecare), m-inozitol – 100 mg/l, zaharoză – 20 g/l şi agar-agar 7 g/l, fără fitoregulatori de creștere. Variabila este reprezentată de sursa de iluminare, tuburi fluorescente și LED-uri (monocrome și diferit colorate): albastru (λ = 470nm), galben (λ = 580nm), verde (λ = 540nm), roșu (λ = 670nm) și LED-uri care emit lumină albă (λ = 510nm) la o intensitate luminoasă de 1000 lux. Am urmărit timp de 90 de zile evoluţia vitroculturilor de R. heliosa și am analizat variabilitatea de reacţie a acestora iar pe baza studiului comparativ putem afirma următoarele: lumina tuburilor fluorecente este mai potrivită pentru morfogeneza vitroplantulelor de R. heliosa, dar procesele de regenerare și organogeză sunt influențate în mod direct de sursa și culoarea luminii, astfel rizogeneza și caulogeneza este favorizează de prezența luminii verde și roșie emisă de LED-uri în timp ce lumina albă și galbenă a tuburilor fluorescente avantajează procesele de caulogeneză și calusogeneză

Invariants of binary forms

We work over the field of complex numbers. Consider the set V_n of binary forms of degree n, i.e., homogeneous polynomials of degree n in two variables. An invariant of V_n is a polynomial in the coefficients of a form in V_n whose value does not change under the action of the group of complex 2x2 matrices with determinant 1 on V_n. In 1893, Hilbert proved that the algebra of invariants of V_n is finitely generated for all n. However, finding explicit sets of generators is in general a difficult problem. They were known for binary forms of degree 8 and less than 7 since the 19th century, but for higher degrees the problem remained open. Over the last 25 years some progress was booked: generators for the invariants of binary forms of degree 7 were found by Dixmier and Lazard, and for the invariants of forms of degrees 9 and 10 by Brouwer and myself. This thesis is organised as follows. In Chapter 2 we introduce definitions and notation that will be used throughout this thesis. In Chapter 3 we present the computational methods that we use for finding generating invariants of binary forms. In Chapter 4 we find the generating invariants of binary forms of degree 2,3,...,10, and give explicit systems of parameters in all these cases. In Chapter 5 we review classical results regarding the invariants of several binary forms. We correct a result of Winter on the generating covariants of V_2+V_5 and results of Gundelfinger and Sylvester on the generating covariants of V_3+V_4. In Chapter 6, extending a result of Popov, we classify the modules whose algebras of invariants have homological dimension less than or equal to 15

Type 1 Diabetes Mellitus and Autoimmune Diseases: A Critical Review of the Association and the Application of Personalized Medicine

Type 1 Diabetes Mellitus (T1DM) is a common hyperglycemic disease characterized by the autoimmune destruction of insulin-producing beta cells of the pancreas. Various attempts have been made to understand the complex interplay of genetic and environmental factors which lead to the development of the autoimmune response in an individual. T1DM is frequently associated with other autoimmune illnesses, the most common being autoimmune thyroid disorders affecting more than 90% of people with T1D and autoimmune disorders. Antithyroid antibodies are present in around 20% of children with T1D at the start of the illness and are more frequent in girls. Patients with T1DM often have various other co-existing multi-system autoimmune disorders including but not limited to thyroid diseases, parathyroid diseases, celiac disease, vitiligo, gastritis, skin diseases, and rheumatic diseases. It is a consistent observation in clinics that T1DM patients have other autoimmune disorders which in turn affect their prognosis. Concomitant autoimmune illness might affect diabetes care and manifest itself clinically in a variety of ways. A thorough understanding of the complex pathogenesis of this modern-day epidemic and its association with other autoimmune disorders has been attempted in this review in order to delineate the measures to prevent the development of these conditions and limit the morbidity of the afflicted individuals as well. The measures including antibody screening in susceptible individuals, early identification and management of other autoimmune disorders, and adoption of personalized medicine can significantly enhance the quality of life of these patients. Personalized medicine has recently gained favor in the scientific, medical, and public domains, and is frequently heralded as the future paradigm of healthcare delivery. With the evolution of the &lsquo;omics&rsquo;, the individualization of therapy is not only closer to reality but also the need of the hour

Sylvester versus Gundelfinger

Let $V_n$ be the ${m SL}_2$-module of binary forms of degree $n$and let $V = V_1 oplus V_3 oplus V_4$. We show that the minimum number of generators of the algebra $R = mathbb{C}[V]^{{m SL}_2}$ of polynomial functions on $V$ invariant under the action of ${m SL}_2$ equals 63. This settles a 143-year old question