A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.
Different types of number theories such as elementary number theory, algebraic number theory and computational number theory; algebra; cryptology; security and also other scientific fields like artificial intelligence use applications of quadratic fields. Quadratic fields can be separated into two parts such as imaginary quadratic fields and real quadratic fields. To work or determine the structure of real quadratic fields is more difficult than the imaginary one.
The Dirichlet class number formula is defined as a special case of a more general class number formula satisfying any types of number field. It includes regulator, 𝓛-function, Dedekind zeta function and discriminant for the field. The Dirichlet’s class number h(d) formula in real quadratic fields claims that we have
for positive d > 0 and the fundamental unit εd of ℚ(). It is seen that discriminant, 𝓛-function and fundamental unit εd are significant and necessary tools for determining the structure of real quadratic fields.
The focus of this paper is to determine structure of some special real quadratic fields for d > 0 and d ≡ 2, 3 (mod 4). In this paper, we provide a handy technique so as to calculate particular continued fraction expansion of integral basis element wd, fundamental unit εd, and so on for such real quadratic number fields. In this paper, we get fascinating results in the development of real quadratic fields.
Santa Rasa-Dzelzkalēja, Svetlana Čapenko, Angelika Krūmiņa, Yung-Cheng Lin and Modra Murovska
Our aim was to estimate the presence of B19V infection markers, the level of cytokines and time period since the appearance of infection in association with ME/CFS clinical symptoms. In 200 ME/CFS patients and 104 control group individuals the presence of B19V-specific IgG/IgM class antibodies, B19V NS1 gene sequence, mRNA expression, viral load and level of cytokines were determined. B19V-specific IgG-antibodies were found in 70% of ME/CFS patients and 67.4% of controls, IgM-antibodies in 8% of patients and in none of controls, B19V genomic sequences in 29% of patients and 3.8% of controls. 58.6% of positive patients had active and 41.4% had latent/persistent B19V infection. B19V NS1 gene expression was detected in 43% of patients. B19V load varied from < 0.2 copies to median 38.2 copies/µg of DNA. According to the antibody pattern, 36% of patients had a recent, and 43% had sustained B19V infection. Patients with the B19V genomic sequence and NS1 specific antibodies significantly more often had lymphadenopathy and multi-joint pain. Onset of the symptoms corresponded to time of appearance of B19V infection. IL-10 and TNF-levels were higher in patients with elevated B19V load. B19V genome 1 was identified in Latvian ME/CFS patients. The results indicated that at least in some cases B19V infection plays an important role in ME/CFS development
Miķelis Birznieks, Iveta Golubovska, Lauris Repša, Inta Čerņavska, Jānis Ābols, Aivars Muste, Igors Ļu and Aleksejs Miščuks
Due to an ageing population, the necessity for hip replacement has grown, and therefore, new options are being sought, such as the Fast-track principle, to improve patient condition, reduce their hospital stay and enhance the hospital’s ability to treat more patients. The aim of this study was to investigate the effects of same-day patient mobilisation on pain, side effects, complications, duration of hospital stay, and recovery after primary hip replacement, using intermediate-acting local anaesthetics in spinal anaesthesia (SA). A prospective, randomised study was conducted at the Hospital of Traumatology and Orthopaedics. Forty-six patients undergoing total hip replacement were selected and divided into two groups. Spinal anaesthesia was performed in study group (P) with 70 mg plain prilocaine. The control group (B) received 18 mg heavy bupivacaine in SA. On the first postoperative day, pain during movement was 2.00 (P) and 3.33 (B) on the Numeric Pain Rating Scale, the duration of hospital stay in the study group was shorter by ~1 day, and patient self-care was better in the study group. When the Fast-track principle is used with intermediate-acting SA and early rehabilitation, it is possible to reduce post-operative pain during movement, reduce the length of stay and improve patient self-care abilities.
Aigars Lācis, Natālija Ezīte, Jānis Šavlovskis, Indulis Kukulis, Roberts Rumba, Eva Strīķe, Edgars Zellāns, Inguna Ļūļaka and Dainis Krieviņš
Patients with peripheral arterial disease (PAD) have substantially impaired health-related quality of life (HR-QoL). Chronic lower limb ischaemia due to the atherosclerotic occlusion of infra-inguinal arteries is one of the most important causes of invalidity among smokers over the age of fifty. Historically, these lesions were treated by open bypass surgery. Less invasive endovascular revascularisation methods are available to treat short lesions, while treatment of long lesions are lacking. Fully endovascular trans-venous femoro-popliteal bypass (PQ Bypass, Inc., Sunnyvale, CA, USA) to treat long femoral lesions has been developed recently. The objective of the study was to evaluate duplex ultrasound (DUS) as a tool to follow up patients after PQ bypass procedure. A prospective clinical study was conducted at one clinical site. DUS of treated arteries and femoral vein was performed before the procedure, 30 days, 6 months, and 12 months in follow-up period by 2 independent radiologists. Ankle-brachial index (ABI) evaluation was performed at all visits. Thirty-five patients (35 limbs) treated with PQ bypass were enrolled in the study. Median age was 63.6 years (ranged 50 to 87 years). There was 100% successful evaluation of all patients at all clinical visits available. Deviation of the DUS results was found within the accepted standard limit between two radiologists. Twelve months after the PQ procedure, 28 (80.0%) PQ stent-grafts were still functioning without DUS signs of stenosis, while seven (20.0%) limbs experienced varying degrees of stent malfunction. PQ stent-graft occlusion was detected in five (14.3%) – 1 (2.9%) patients at one-month follow-up, 3 (8.6%) at six months and 1 (2.9%) at twelve months follow-up period, respectively. PQ stent-graft proximal junction stenosis was detected in one patient (2.9%) at six months and distal junction stenosis in one patient (2.9%) at twelve months follow-up, respectively. Despite of graft occlusion found with DUS, two patients had no severe worsening of post-operative ABI. DUS is a reliable method to evaluate patients after PQ bypass procedure and has higher sensitivity than ABI to follow-up patients after PQ procedure, especially in asymptomatic stent stenosis. Regular and timely use of DUS during the postoperative period may help to recognise potential complications and provide effective treatment..
Baiba Ieviņa, Nils Rostoks, Naeem H. Syed, Andrew J. Flavell and Gederts Ievinsh
Genetic diversity among 13 northern populations of the declining coastal plant Eryngium maritimum L. at the northernmost extent of the species distribution range was studied using retro-transposon-based SSAP molecular markers. Diversity indices varied extensively among populations; some showing extremely low diversity whereas other populations exhibited moderate amounts of genetic variation. Differentiation among populations was highly variable as well. Interestingly, differentiation among northern populations was not influenced strongly by geographic distance. Closely situated populations were often more divergent than more distant populations suggesting other factors may be responsible for genetic structuring of E. maritimum populations. We propose that the following genetic and environmental factors combine together in a complex relationship to mould the present genetic structure of E. maritimum populations in this region: (1) historic biogeographical processes; (2) local environmental conditions at each site; (3) success of sexual reproduction and proportion of clonal propagation; (4) size of the population and influence of genetic drift; (5) level of fragmentation and isolation. Lastly, we suggest that the sustainable existence of Latvian populations is seriously threatened, unless recommended conservation measures are implemented.
Marta Laizāne, Ieva Saulīte, Sandra Feierābende and Ingrīda Rumba-Rozenfelde
Vitamin D deficiency is common and widespread globally. Vitamin D has an immunomodulatory effect, but it is still unclear whether its deficiency is associated with higher disease activity. The aim of this retrospective study was to determine the serum concentration of vitamin D in children with paediatric arthritis (juvenile idiopathic arthritis and reactive arthritis). Prevalence of hypo-vitaminosis D among 98 children with juvenile idiopathic arthritis and reactive arthritis was determined and association between serum concentration of vitamin D and disease activity markers was found. Prevalence of vitamin D deficiency among children included in this study was 69.07%. Children with juvenile idiopathic arthritis had a significantly lower vitamin D level than children with reactive arthritis. There was a statistically significant moderate negative correlation between serum concentration of vitamin D and patient age, as well as a weak negative correlation between vitamin D level and patient body mass index. The significant correlations found between vitamin D level and inflammatory markers indicate that further research on the role of vitamin D in disease activity is needed.
This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.
Artis Gulbis, Edgars Ginevičs, Agnese Ozoliņa, Kaspars Ruks, Indulis Vanags and Konstantīns Kalnbērzs
Surgical intervention in cervical disease can relieve neurological symptoms and improve life quality. This study aimed to analyse retrospective data of microscope-assisted anterior cervical discectomy and fusion (ACDF) surgeries. The retrospective study was carried out at the ORTO clinic, Rīga, Latvia, from 2013 to 2017. Data from 198 patients were extracted retrospectively. Data on patient gender, age, diagnosis, extent of operation, type of cage and the overall height of the implants were used. Comparative analysis was carried out with the SPSS 22 software. P < 0.05 represented statistical significance. During the study period, 198 elective ACDF were carried out with increasing number of surgeries: 25 cases in 2013, 43 in 2014, 38 in 2015, 44 in 2016, and 48 in 2017. ACDF were significantly more often performed for females (n = 117, 59%) compared to males (n = 81, 41%; p < 0.003). Women were older with an average age of 50 ± 1 years than men (age 46 ± 1; p = 0.007). The mean surgery time was 1.5 ± 1 hours and the mean hospitalisation time was 3 ± 1 days. Four types of cages were used in similar number of operation: Cervios Peek Chronos C (24%), Syncage C (21%), EIT 3D print (29%), Cervios C Peek (26%); p = 0.2, regardless of patient age or gender. Most often, in 98 cases, the overall height of implants was 6–10 mm. The maximal height was 22 mm, where two patients underwent three-level, and one had a four-level discectomy. The most prevalent disc lesion levels were C5/6 and C6/7, followed by C4/5 and C3/4. One- and two-level discectomies were performed in similar numbers: 95 and 81 cases. However, only 20 patients underwent three level and two patients had four level discectomies in 2016 and 2017. Two level discectomy at C5/6, C6/7 was carried out significantly more often for women (55 vs. 26; p = 0.01), and for men 1-level lesion was more common in C6/7; p = 0.04. The overall incidence of cage subsidence was 5.5%, and the highest incidence was 24% when a Syncage C was used. The ACDF appears to be performed increasingly more often, particularly, in females. The most frequent operation was in one or two cervical levels; including level C6/7 in both genders. In the last years, three- and four-level cervical discectomies have become one of the surgical opportunities. Choice of cage was not influenced by patient gender and age, while cage biophysical and biochemical properties may influence the choice.
The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.