Proceedings of the Bulgarian Academy of Sciences <p>Founded in 1948 by academician Georgy Nadjakov, "Comptes rendus de l’Académie bulgare des Sciences" is also known as "Доклади на БАН","Доклады Болгарской академии наук" and "Proceedings of the Bulgarian Academy of Sciences".</p> <p>If applicable, the name of the journal should be abbreviated as follows: C. R. Acad. Bulg. Sci. (according to ISO.)</p> <p><big><strong>Related subjects:</strong></big></p> <p class="condensed">Astronomy, Mathematics, Physics, Chemistry, Biology, Geology, Geophysics, Space Sciences, Engineering Sciences, Physical Geography, Medicine, Agricultural Sciences.</p> <p class="condensed">The manuscripts should contain only unpublished data in the respective scientific field. They can further be expanded to be published elsewhere. All manuscripts are subject to peer review and copy editing.</p> <p><strong><big>2002-2021 website:</big></strong></p> <p>The site with the archive of <em>Comptes rendus de l’Académie bulgare des Sciences</em> - 2002 to 2021 is <a href="" target="_blank" rel="noopener">still accessible at that address.</a></p> „Prof. Marin Drinov“ Academic Publishing House en-US Proceedings of the Bulgarian Academy of Sciences 1310-1331 <p>Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences</p> <p>Copyright is subject to the protection of the <em>Bulgarian Copyright and Associated Rights Act</em>. The copyright holder of all articles on this site is Proceedings of the Bulgarian Academy of Sciences. If you want to reuse any part of the content, please, contact us.</p> Some Lacunary Power Series and Mahler’s Um-numbers in p-adic Domain <p>In this paper, we consider some lacunar power series in <em>Q<sub>p</sub></em>, where <em>p</em> is a prime number. We obtain some results about lacunary power series with rational coefficients for <em>U<sub>m</sub></em>-number arguments in <em>Q<sub>p</sub></em>. We determined whether the values of the considered lacunar power series belong to a certain field of algebraic numbers or to the set of transcendental numbers in <em>Q<sub>p</sub></em>. Also, we find similar results for lacunary power series with <em>p</em>-adic algebraic coefficients.</p> Fatma Çalışkan Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 477 485 10.7546/CRABS.2022.04.01 Gradient almost Para-Ricci-like Solitons on Para-Sasaki-like Riemannian Pi-manifolds <p>Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar curvatures of the considered both metrics are equal and constant and its Ricci tensor is a constant multiple of the vertical component. Explicit example of a 3-dimensional para-Sasaki-like Riemannian Π-manifold is provided in support of the proved assertions.</p> Hristo Manev Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 486 494 10.7546/CRABS.2022.04.02 Polynomial and Multinomial Coefficients in Terms of Number of Shortest Paths <p>The binomial coefficients show, in fact, the number of shortest paths in the square grid if only grid paths, i.e., paths on the grid lines, are allowed, and they also give the number of shortest paths in the hexagonal grid. When diagonal steps are also allowed in the square grid, the number of shortest paths can be described by trinomial coefficients. They form a triangle where three neighbour elements in the previous row are summed. We consider also further generalisations of such triangles and their elements, quadrinomial and <em>n</em>-nomial coefficients. In this context, <em>n</em>-nomial coefficients of <em>n</em>-nomial expansions represent the numbers of paths between the top and the actual position when <em>n</em> different types of steps are allowed to use, e.g., at trinomial coefficients three types of steps. Formulae to calculate trinomial, quadrominal and <em>n</em>-nomial coefficients are shown based on trinomial, quadrominal and <em>n</em>-nomial expansions, where the power of the sum of more than two items is computed, respectively. Multinomial expansions are also related. We give also a comparison of those values known as various ways of generalizations of the binomial coefficients.</p> Bashar Khassawneh Benedek Nagy Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 495 503 10.7546/CRABS.2022.04.03 Spectral Properties of Copper(II) bis-monensinate <p>The polyether ionophorous antibiotic monensic acid A (MonH.H<sub>2</sub>O) reacts with copper(II) ions in the presence of a weak base (Et<sub>4</sub>NOH) to form mononuclear coordination species of composition [Cu(Mon)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub>]. The complexation process in solution was studied by synchrotron radiation circular dichroism (SRCD). The isolated complex was characterized using infrared spectroscopy (IR), nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR). The copper ion is placed in an octahedral environment composed of two deprotonated antibiotic monoanions and two water molecules. The monensinates are cis-oriented with respect to the metal(II) centre, acting bidentately through a monodentate carboxylate function and a hydroxyl group, both placed at the opposite ends of the ligand structure. The copper(II) cations do not enter the hydrophilic cavity of monensin. Instead it is occupied by water molecules which complete the octahedral inner coordination sphere of the complex and stabilize the “head-to-tail” chelates of the antibiotic by intramolecular hydrogen bonds.</p> Ivayla Pantcheva Radoslava Stamboliyska Ahmed Nedzhib Petar Dorkov Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 519 526 10.7546/CRABS.2022.04.06 Oxidized Lipids Control Lipid Order and Phospholipase A2 Activity in Model Membranes <p>Oxidative stress is an important etiologic factor in the pathogenesis of various diseases. The formation of oxidized phospholipid species in vivo induces membrane remodelling with direct pathological implications with a prominent inflammatory component. Secretory phospholipases A<sub>2</sub> (sPLA<sub>2</sub>) are involved in the regulation of inflammation and immune response. Their activity is highly dependent on the lipid membrane composition, structure and organization. In this work, we studied the impact of oxidized phosphatidylcholines (OxPCs) on the membrane lipid order and the sPLA<sub>2</sub> activity. The effects of two of the most physiologically active OxPCs, 1-palmitoyl-2-(5′-oxo-valeroyl)-<em>sn</em>-glycero- 3-phosphocholine (POVPC) and 1-palmitoyl-2-glutaroyl-<em>sn</em>-glycero-3- phosphocholine (PGPC) were compared using 1-palmitoyl-2-oleoyl-<em>sn</em>-glycero- 3-phosphocholine (POPC) vesicles. Both OxPCs reduce the membrane lipid order and sPLA<sub>2</sub> activity at physiological temperature. Moreover, these changes depend on the chemical nature of the oxidized chains.</p> Vesela Yordanova Rusina Hazarosova Victoria Vitkova Aneliya Kostadinova Miglena Angelova Albena Momchilova Plamen Krastev Galya Staneva Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 581 589 10.7546/CRABS.2022.04.13 The Utility of Preimplantation Genetic Test in Couples with History of Infertility and Pregnancy Loss <p>Preimplantation genetic test (PGT) is cutting-edge technology for early detection of genetic abnormalities in embryos prior to their implantation in the uterus. PGT prevents the transfer of affected embryos during in vitro fertilization (IVF) procedures and termination of pregnancy. In our study we report the results from 185 couples with history of infertility and pregnancy loss that had undergone IVF procedures with PGT. Trophectoderm biopsy was carried out on 497 blastocyst stage embryos originating from 231 oocyte retrieval cycles. Array-based comparative genomic hybridization (aCGH) and next-generation sequencing (NGS) were subsequently performed. One hundred and ninety-six embryos had balanced profile (40.16%) and 292 embryos showed unbalanced profile (59.84%). Embryo transfer was performed in 109 cases (58.92%) and biochemical pregnancy was reported in 33.03%. Live birth rate was 29.36% and pregnancy loss occurred in 3.67% of cases. Our results show that PGT reduces the number of meaningless transfers, eliminates the trauma of termination of desired pregnancy and possible medical complications. In couples with reproductive failure PGT decreases the risk for pregnancy loss, increases the chance of conceiving with a chromosomally balanced embryo and live birth of a healthy offspring per transfer.</p> Savina Hadjidekova Slavyana Staykova Rada Staneva Maria Pancheva Maria Serafimova Kristina Nikolova Draga Toncheva Georgi Stamenov Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 590 595 10.7546/CRABS.2022.04.14 C-Reactive Protein/Albumin Ratio in Patients with Type 2 Diabetes Mellitus <p>Type 2 diabetes mellitus (T2DM) is an inflammatory condition. C-reactive protein (CRP) is a well-known inflammatory marker for demonstrating systemic inflammation in T2DM. We aimed to compare the diagnostic value of CRP and C-reactive protein to albumin ratio (CAR) in discriminating T2DM patients and healthy controls and to investigate the association of CAR and glycemic control markers. This cross-sectional retrospective study included 173 T2DM patients and 104 healthy control subjects. Serum albumin and CRP levels were measured with spectrophotometric and nephelometric methods, respectively. CAR was calculated by dividing CRP level by albumin level. The median (interquartile range, IQR) CAR in the T2DM patients was significantly higher than those in the controls (0.15 (0.26) vs. 0.06 (0.20), <em>p</em> = 0.002, respectively). In receiver operating characteristics curve analysis (ROC), CAR &gt; 0.0653 had 77.21% sensitivity and 52.44% specificity in discriminating T2DM. The area under ROC curve for CAR was 0.623 (95% CI =0.544–0.701, <em>p</em>=0.002), which was similar to CRP. A positive correlation was found between CAR and body mass index, fasting blood glucose and HbA1c levels. As a result, CAR demonstrated poor sensitivity and specificity for discriminating T2DM patients from healthy subjects and it has little diagnostic utility in diabetes.</p> Zeynep Caliskan Yalcin Hacioglu Nurgul Bulut Yildiz Dincer Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 596 605 10.7546/CRABS.2022.04.15 Prevalence in Apparently Healthy Postmenopausal Women of More than 1 SD T-score Difference between Two Adjacent Lumbar Spine Vertebrae (L1–L4) without Any Identifiable Cause <p>The presence of isolated low bone density of a single lumbar vertebra (difference of above 1 SD T-score between two adjacent vertebrae without a probable explanatory reason) seems to be one of the unsolved issues in clinical densitometry. The present study aims to investigate the epidemiology of the latter mentioned difference in BMD. In a prospective manner 4027 apparently healthy Bulgarian women between 50 and 65 years of age underwent а scan of the lumbar spine (L1–L4) on a DXA machine – Hologic Discovery A. The data were collected and analysed with the statistical package SPSS. In the observed group the incidence of the difference of above 1 SD T-score between two adjacent lumbar vertebrae without a causal visible abnormality is quite low – 1.34% (<em>n</em> = 54). In the study population, the mean T-score was 1.49 (±0.469 SD) and the difference itself was between – 1 and – 2.6 SD T-score. A consensus statement and a guideline for further clinical management of patients with this finding are necessary to be created. </p> Kristina Sirakova Antonina Gerganova Nataliya Temelkova Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 606 611 10.7546/CRABS.2022.04.16 Dental Status of Active Age Population in the Republic of Bulgaria <p>Dental health is an important public health component. There is a number of dependencies between the demographic and social characteristics of the population and its dental status. The purpose of the study is to examine the dental status of the active age population in the Republic of Bulgaria and to define its dependence on social and demographic factors. Epidemiologic study and inquiry survey were conducted among 416 Bulgarian citizens aged 18–65 years in six district towns for achieving the aim. The results were processed and subjected to statistical analysis with significance factor 95% (<em>p</em> = 0.05). Prevalence per persons (E<sub>P</sub>) for the studied sample is 98.56%, teeth prevalence (E<sub>T</sub>) has an average value of 52.7%, while the dental caries intensity (DMFT) is 16.25. Caries incidence and intensity increases with age as a result of a proportional increase in the number of obturated and extracted teeth with patients’ ageing. The average number of treated teeth is bigger in individuals with higher education and at the same time, this group has lower average number of extracted teeth. Lower average number of extracted teeth is also reported in persons with high income compared to those on minimal wages and parallel the average number of obturated teeth increases proportionally to the income increase. There is distinct dental status dependence in the active age Bulgarian population on demographic and social factors. Persons, paying regular visits to the dental office, have lower number of caries and extracted teeth, which supports the importance of dental prophylaxis.</p> Stanislav Nenov Petar Bozhinov Nikolai Hristov Boyko Bonev Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 612 619 10.7546/CRABS.2022.04.17 Dark Energy is Dark Matter below Absolute Zero in Black Holes <p>It is proven that the Clapeyron–Mendeleev equation, originally discovered for gases with large entropy, describes the state of dark matter/energy due to the enormous self-gravitation. It is shown that the dark matter exists as compact cold neutrino stars at positive temperature with size twice the Schwarzschild radius. In contrast, the dark energy is dark matter at temperature below the absolute zero, which is locked entirely in black holes, where the pressure is negative as required for the Universe intrinsic expansion. The derived dark phase diagram predicts negative critical temperatures for the Big Bang and the Big Rip of black holes. </p> Roumen Tsekov Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 504 509 10.7546/CRABS.2022.04.04 Investigation of the Gyrotropy in the Spectral Region of the Absorption "Shoulder" of the Oxide Crystal Bi12SiO20 <p>This paper presents the research of the gyrotropy of a pure Bi$$_{12}$$SiO$$_{20}$$ (BSO) and doped Bi$$_{12}$$SiO$$_{20}$$:Al (BSO:Al) crystals in the spectral region of "absorption shoulder" using measurements of the spectra of the natural optical rotation, the magneto-optical rotation and the optical spectroscopy. It is shown that the difference in the absorption of the BSO and BSO:Al crystals is related to the presence of two types of defects in the crystals BSO:Al – impurities $$\rm Al_{Si}^{3+}$$ in $$\rm[Al_{Si}^{3+}O_4]$$ and $$\rm Bi_{Si}^{3+}$$ in $$\rm[Bi_{Si}^{3+}O_4]$$. A "red-shift" of the optical rotation spectrum of BSO:Al crystals has also been observed relative to the optical rotation spectrum of BSO crystals.</p> Todor Dimov Iliya Iliev Antonina Hristova Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 510 518 10.7546/CRABS.2022.04.05 Spatial Sampling Design for the Geogenic Radon Potential Survey in Sliven Province, Bulgaria <p>The development of a methodology for the geogenic radon potential (GRP) mapping based on soil gas radon and soil gas permeability field measurements is among the main objectives in the determination of “radon priority areas” in Bulgaria. One of the key elements of the methodology is to define as accurately as possible, areas of risk for the presence of radon gas (222Rn) on the map. This study presents an approach to spatial sampling for the geogenic radon potential survey in Sliven Province, Bulgaria. The district is characterised by its very complex geological settings, represented by rocks of different age and mineral and chemical compositions. The proposed methodology defined a sampling frame of province radon map, prepared on the base of indoor radon measurement and the complex sampling scheme of random points. The parcel-level GIS was used for establishing the sample frame of 5×5 km <em>polygons</em> on the territory of the province. The IBM SPSS <em>Complex Samples Module</em> was applied for planning the survey’s <em>polygons</em> by drawing sample units according to the spatial design. The spatial relationship between indoor radon concentration and geological information was analysed for the sampling scheme construction by <em>the polygons</em>. The <em>latter</em> serve as sampling units, allowing both indoor radon concentration and geological data to be linked. The results show that the applied spatial sampling approach allows controlling the specific environmental conditions, in terms of their specificity, variability, and distribution. </p> Dimitar Antonov Kremena Ivanova Bistra Kunovska Desislava Djunakova Iren Ilieva Polina Andreeva Sava Kolev Aleksey Benderev Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 561 569 10.7546/CRABS.2022.04.11 Callus via Shoot Organogenesis and Plant Regeneration of Stevia rebaudiana Bertoni <p><em>Stevia rebaudiana</em> Bertoni is important medicinal plant which is native between southern Brazil and northern Paraguay. A reliable protocol for shoot organogenesis and regeneration was developed for an antidiabetic medicinal plant species. Regeneration via indirect shoot organogenesis was established from two types of explant (leaf and stem) on MS medium [<sup>1</sup>] with different concentrations and combinations of plant growth regulators (PGR) such as 2,4-dichlorophenoxyacetic acid (2,4-D), 6-benzylaminopurine (BAP) and gibberellic acid (GA<sub>3</sub>) for inducing organogenic callus of <em>S. rebaudiana</em>. In the present investigation the highest percentage of response was shown by 90% and 80% callogenesis from leaf and stem explants on MS medium supplemented with 2.0 mg/l 2,4-D + 0.5 mg/l BAP + 0.5 mg/l GA<sub>3</sub> (MSC<sub>3</sub>) was observed. The high frequency of regenerants was observed from <em>S. rebaudiana</em> leaves at 0.5 mg/l 2,4-D + 2.0 mg/l BAP + 0.5 mg/l GA<sub>3</sub> (MSR<sub>3</sub>). Optimal shoot multiplication and rooting were obtained on 2.0 mg/l BAP and 0.1 mg/l indole- 3-butyric acid (IBA), respectively, followed by successful acclimatization of regenerants (90% survival) to greenhouse condition. The purpose of this study was to establish a reliable <em>S. rebaudiana</em> regeneration protocol that can be used to facilitate the cultivation, propagation and planting of this plant species. </p> Ely Zayova Trendafil Nedev Ira Stancheva Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 620 628 10.7546/CRABS.2022.04.18 In situ and Ex situ Investigations on Breeding Systems and Pollination of Sideritis Scardica Griseb. (Lamiaceae) in Bulgaria <p><em>Sideritis scardica</em> is a short living perennial herb. This Balkan endemic grows in the higher parts of the mountains of Bulgaria, Albania, Greece, and Republic of North Macedonia. It is an endangered species and medicinally valuable plant. <em>S. scardica</em> has been successfully cultivated lately in Bulgaria and propagated by seed. This study presents preliminary in situ and ex situ data on the factors that control the seed production of <em>S. scardica. </em>Investigations were conducted in six study sites (three in situ and two ex situ) in the Rhodopes and one ex situ study site in the foothills of Pirin Mt in 2008 and 2019. The field experiments with enclosed flowers revealed that spontaneous self-pollination does not occur and insect pollen vectors are necessary. The pollinators of <em>S. scardica</em> were polylectic insects such as bumblebees (both in situ and ex situ) and honeybees (only on the big ex situ cultivated fields). Flowers were visited mostly for nectar as a reward and the pollen baskets were filled mainly by the pollen adhered on the pollinators’ body. The protection of wild populations of this plant species as well as its successful cultivation depends on the protection of its pollinators.</p> Hristo Valchev Ekaterina Kozuharova Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 527 535 10.7546/CRABS.2022.04.07 Contribution to the Knowledge of Bromus Diandrus–Rigidus (Poaceae) Polyploid Complex in the Bulgarian and Romanian Floras <p>Comparative morphological and ploidy level survey of the polyploid complex <em>B. diandrus-rigidus</em> in the Bulgarian and Romanian floras was performed. Critical examination of the morphology of the collected specimens revealed <em>B. diandrus</em> is represented in both floras. The species has already been reported for Romania under the name <em>B. rigidus</em>. For Bulgaria, the species has been very recently reported on a conference poster with a single gathering from 2020. Here, we provide more records of the species along the whole Bulgarian Black Sea coast floristic region, with the oldest gathering dating back to 2003. Ploidy level estimation of the Bulgarian accessions by flow cytometry revealed all studied populations are octoploid which is congruent with data from elsewhere, and confirms <em>B. diandrus</em> is present in the Bulgarian flora. For both the Bulgarian and Romanian floras alien status of the species has been inferred. </p> Stoyan Stoyanov Gavril Negrean Vladimir Vladimirov Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 536 544 10.7546/CRABS.2022.04.08 Species Status of Ragworm Populations (Nereididae: Tylorrhynchus Sp.) Exploited as a Human Specialty Based on Their Molecular Analyses in the Northern Coast of Vietnam <p>In the traditional culinary culture of Vietnam, the ragworms (Nereididae) are an ancient and well-known delicacy (<em>Chả rươi in Vietnamese</em>) of great nutritional and economic value. In order to determine their species status, distribution, and sustainable control, a comparative molecular genetic analysis was carried out in 2018--2019. It comprised of ragworm populations along the northern coast including Quang Ninh, Hai Phong, Hai Duong, Thai Binh and Nam Dinh, 20.0, 14.5, 34.0, 26.0 and 17.0 km from the sea, respectively. We found that all of them belong to one and the same species named <em>Tylorrhynchus</em><em> heterochaetus</em> (Quatrefages, 1866). The ragworm in the Tu Ky area of Hai Duong province has the farthest distribution in the mainland, and was among the ragworm groups with the largest morphological measurements. Salinity and inland environmental conditions are likely factors influencing the morphological development of ragworm populations in this area. This may be the reason Tu Ky ragworms have been labelled a specialty dish in Vietnam dating back to ancient history.</p> Vu Quang Manh Nguyen Ha Thi Sakkouna Phommavongsa Tra Ha My Thu Lai Hien Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 545 553 10.7546/CRABS.2022.04.09 On the Pathogenicity of Metarhizium Pemphigi against Ips Typographus L. <p>Efficacy of entomopathogenic fungus <em>Metarhizium</em> <em>pemphigi</em> was evaluated against <em>Ips typographus</em> adults in a laboratory bioassay for the first time. A series of four conidial concentrations (2×10<sup>4</sup>–2×10<sup>7</sup> conidia/ml) were used. The cumulative mortality caused by <em>M. pemphigi</em> varied between 75% and 100% ten days post-treatment, with LC<sub>50</sub> value of 2.9×10<sup>3</sup> conidia/ml and LC<sub>90</sub> value of 6.4×10<sup>4</sup> conidia/ml. The median lethal time (LT<sub>50</sub>) of treated beetles depended on conidial concentrations and ranged from 1.78 to 5.98 days. Pathogenicity of <em>M. pemphigi</em> was reported for the first time and the tested strain was found to be promising for further evaluation in terms of management options against the spruce bark beetle. </p> Danail Takov Marek Barta Teodora Toshova Danail Doychev Daniela Pilarska Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 554 560 10.7546/CRABS.2022.04.10 An Improved Seventh Order Hermite WENO Scheme for Hyperbolic Conservation Laws <p>A seventh order Hermite weighted essentially non-oscillatory (HWENO) scheme [<sup>1</sup>] has been used successfully to solve hyperbolic conservation laws. However, the scheme could not achieve the optimal order of accuracy at critical points. In this paper, we propose a new central seventh order HWENO scheme. It involves seventh order HWENO reconstruction [<sup>1</sup>] and the central-upwind flux [<sup>2, 3</sup>]. For the ideal weights we used the central procedure presented in [<sup>4</sup>] and for nonlinear weights we extend the strategy proposed in [<sup>5, 6</sup>]. For time integration, the seventh order linear strong-stability-preserving Runge–Kutta (<em>ℓSSPRK</em>) scheme is used. The resulting scheme combines the advantages of both the improved and Hermite central schemes, e.g., compactness, improving the convergence and accuracy at critical points, decreasing the dissipation near discontinuities especially for long time evolution problems; it is simple to implement and attains seventh order accuracy. Many numerical tests are presented to validate the performance of the proposed scheme.</p> Yousef Zahran Amr Abdalla Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences 2022-05-02 2022-05-02 75 4 570 580 10.7546/CRABS.2022.04.12