Development and validation of a novel nomogram for predicting overall survival patients with neuroblastoma.

PURPOSE: The aim of this study was to develop a nomogram specially for predicting overall survival (OS) for Chinese patients with neuroblastoma (NB). METHODS: Patients with pathologically confirmed NB who were newly diagnosed and received treatments at our hospital from October 2013 to October 2021 were retrospectively reviewed. The nomogram for OS were built based on Cox regression analysis. The validation of the prognostic model was evaluated by concordance index (C-index), calibration curves, and decision curve analyses (DCAs). RESULTS: A total of 254 patients with NB were included in this study. They were randomly divided into a training cohort (n = 178) and a validation cohort (n = 76) at a ratio of 7:3. Multivariate analyses revealed that prognostic variables significantly related to the OS were age at diagnosis, bone metastasis, hepatic metastasis, INSS stage, MYCN status and DNA ploidy. The nomogram was constructed based on above 6 factors. The C-index values of the nomogram for predicting 3-year and 5-year OS were 0.926 and 0.964, respectively. The calibration curves of the nomogram showed good consistency between nomogram prediction and actual survival. The DCAs showed great clinical usefulness of the nomograms. Furthermore, patients with low-risk identified by our nomogram had much higher OS than those with high-risk (p < 0.001). CONCLUSION: The nomogram we constructed exhibited good predictive performance and could be used to assist clinicians in their decision-making process.

Intralayer Synchronization and Interlayer Quasisynchronization in Multiplex Networks of Nonidentical Layers.

In this article, we discuss synchronization in multiplex networks of different layers. Both the topologies and the uncoupled node dynamics in different layers are different. Novel sufficient criteria are derived for intralayer synchronization and interlayer quasisynchronization, in terms of the coupling matrices, the coupling strengths, and the intrinsic function of the uncoupled systems. We also investigate interlayer synchronization of multiplex networks with identical uncoupled node dynamics. Finally, we give some numerical examples to validate the effectiveness of these theoretical results.

[The Effects of IGHG1 on the Proliferation and Apoptosis of Human Acute Myeloid Leukemia THP-1 Cells].

OBJECTIVE: To investigate the effects of the immunoglobulin G1 heavy chain constant region (IGHG1) on the proliferation and apoptosis of acute myeloid leukemia (AML) THP-1 cells and its possible mechanism of action. METHODS: Human AML THP-1 cells were cultured in vitro and divided into control (normally cultured THP-1 cells), pcDNA3.1 ï¼»THP-1 cells transfected with IGHG1 overexpression (pcDNA3.1-IGHG1) negative control plasmidï¼½, pcDNA3.1-IGHG1 (THP-1 cells transfected with plasmid containing pcDNA3.1-IGHG1), LY364947 ï¼»transforming growth factor-ß (TGF-ß)/signal transduction protein (Smad) inhibitor LY364947 20 µmol/L treated THP-1 cellsï¼½, si-NC ï¼»THP-1 cells transfected with IGHG1-small interfering RNA (siRNA) negative controlï¼½, si-IGHG1 (THP-1 cells transfected with IGHG1-siRNA), and si-IGHG1+LY364947 (IGHG1-siRNA and LY364947 co-treated THP-1 cells) a total of 7 groups. Fluorescence quantitative PCR was used to detect the expression of IGHG1 and immunoglobulin G (IgG) mRNA of THP-1 cells in each group; CCK-8 was used to detect THP-1 cells proliferation activity; flow cytometry was used to detect THP-1 cells apoptosis and cell cycle in each group; Western blot was used to detect the THP-1 cells proliferation, apoptosis and the expression of TGF-ß/Smad signaling pathway related proteins. RESULTS: Compared with the control group, after overexpression of IGHG1, the expression of IGHG1 and IgG mRNA, cell proliferation viability, S phase cell ratio, expressions of Cyclin D1, B cell lymphoma-2 (Bcl-2), IgG, TGF-ß1, phosphorylated Smad3 (p-Smad3)/Smad3 protein in THP-1 cells were significantly increased (P<0.05), the apoptosis rate, G0/G1 phase cell ratio, expression of p21, Bcl-2 related X protein (Bax), Caspase-3 protein were significantly reduced (P<0.05); after inhibiting TGF-ß/Smad signaling pathway or silencing IGHG1, the expression of IGHG1 and IgG mRNA, cell proliferation viability, S phase cell ratio, expression of Cyclin D1, Bcl-2, IgG, TGF-ß1, p-Smad3/Smad3 protein in THP-1 cells were significantly reduced (P<0.05), the apoptosis rate, G0/G1 phase cell ratio, expressions of p21, Bax, and Caspase-3 protein were significantly increased (P<0.05); and compared with silencing IGHG1, after co-treatment of IGHG1 gene silencing and TGF-ß/Smad pathway inhibition, the expression of IGHG1 and IgG mRNA, cell proliferation viability, S phase cell ratio, expressions of Cyclin D1, Bcl-2, IgG, TGF-ß1, p-Smad3/Smad3 protein in THP-1 cells were significantly reduced (P<0.05), the apoptosis rate, G0/G1 phase cell ratio, expression of p21, Bax, and Caspase-3 protein were significantly increased (P<0.05). CONCLUSION: Silencing IGHG1 gene can down-regulate the expression of IgG, inhibit the proliferation of human AML THP-1 cells, block cell cycle progression, and induce cell apoptosis; its mechanism may be related to the inhibition of the TGF-ß/Smad pathway activation.

Case report: Successful immunomodulators combined with electromagnetic field therapy in a patient with methazolamide-induced Steven Johnson syndrome/toxic epidermal necrolysis overlap.

Methazolamide is used to treat patients with glaucoma. However, as a sulfonamide derivative, methazolamide shares the same adverse reaction profile as other sulfa-based medications. Stevens-Johnson syndrome (SJS) and toxic epidermal necrolysis (TEN) are rare delayed-type hypersensitivity cutaneous reactions with high morbidity and mortality. Here, we report a severe SJS/TEN overlap syndrome in an 85-year-old Chinese male patient who received methazolamide 25 mg twice daily for his left eye glaucoma. The causal relationship between SJS/TEN and methazolamide was categorized as "highly likely" on the algorithm for assessing drug causality for epidermal necrolysis. In addition to the treatments with methylprednisolone and immunoglobulin, we used a special electromagnetic spectrum therapeutic apparatus to provide skin wound care. The patient had a thoroughly satisfying recovery. This is the first case report to use electromagnetic field therapy in a patient with SJS/TEN. We share our experience here and suggest that electromagnetic field therapy can provide advanced skin wound care and facilitate the recovery of SJS/TEN.

Feasibility of high-throughput drug sensitivity screening (HDS)-guided treatment for children with refractory or relapsed acute myeloid leukemia.

Relapsed/refractory (rel/ref) acute myeloid leukemia (AML) has a very high mortality rate. At present, hematopoietic stem cell transplantation (HSCT) is the most effective treatment for rel/ref AML. The remission of the primary disease before HSCT is crucial for the transplantation to be effective. Therefore, it is critical to choose a suitable type of chemotherapy before HSCT. Here, we recorded the outcomes of high-throughput drug sensitivity screening (HDS) in children with rel/ref AML. Thirty-seven pediatric rel/ref AML patients who received HDS from September 2017 until July 2021 were analyzed retrospectively. Most of the patients (24 patients, 64.9%) had adverse cytogenetics. Two patients had rel/ref AML with central nervous system leukemia. The complete remission (CR) rate was 67.6%. Eight patients developed IV grade bone marrow suppression. Twenty-three patients (62.2%) underwent HSCT. The 3-year overall survival (OS) and EFS rates were 45.9% and 43.2%, respectively. Infection in the myelosuppression stage was the main cause of death. The outcome of HDS was superior to the commonly reported rates. These results suggest that HDS may be a novel treatment option for pediatric patients with rel/ref AML, and it is a promising transitional regimen prior to HSCT.

[Recent research on chimeric antigen receptor T cells in children with refractory/relapsed acute lymphoblastic leukemia]. / 嵌合抗原受体Tç»†èƒžåœ¨å„¿ç«¥å¤å‘éš¾æ²»æ€§æ€¥æ€§æ·‹å·´ç»†èƒžç™½è¡€ç— ä¸­çš„ç ”ç©¶è¿›å±•.

At present, the treatment of refractory/relapsed acute lymphoblastic leukemia is still in a difficult situation, and even if the intensity of chemotherapy is increased or it is combined with hematopoietic stem cell transplantation, some children may have a poor prognosis and a short survival time. Chimeric antigen receptor T-cell (CAR-T) immunotherapy uses genetically engineered T cells and does not rely on the human leukocyte antigen pathway to recognize tumor-specific antigens, and then CAR-T cells bind to target antigen cells to trigger immune response, thereby exerting a sustained anti-leukemia effect. As the most rapidly developed tumor immunotherapy, major breakthroughs have been made for CAR-T cells in the treatment of various hematological tumors, but there still lacks a comprehensive system for the research, development, and production of CAR-T cells and standardized diagnosis and treatment protocols in China. This article reviews the recent research on CAR-T cells in children with refractory/relapsed acute lymphoblastic leukemia.

Analysis of RAS gene mutations in adverse events during first induction chemotherapy in childhood acute lymphoblastic leukemia.

Background: The rat sarcoma virus (RAS) pathway controls cell proliferation, differentiation, and apoptosis, which have been implicated in the pathogenesis of various hematological malignancies. Prognostic importance of RAS gene mutation, relatively frequently in childhood acute lymphoblastic leukemia (ALL), has been debated. We aimed to study RAS gene mutation profile and prognosis in 93 children with newly diagnosed ALL. Methods: We retrospectively analyzed clinical characteristics, treatment, and outcomes of 93 ALL children during first induction chemotherapy in Anhui Provincial Children's Hospital under the Chinese Children's Leukemia Group-acute lymphoblastic leukemia 2018 (CCLG-ALL-2018). All genomic DNA samples were obtained from bone marrow mononuclear cells upon new diagnosis. RAS gene mutation was performed by polymerase chain reaction (PCR). All children were stratified into standard-, medium-, and high-risk groups, and then treated with risk-based regimens according to CCLG-ALL-2018 protocol. Results: Of 93 ALL children, 26 (27.9%) were positive for RAS mutation, among whom 19 had N-RAS mutation, 8 had K-RAS mutation, and 1 had a double mutation. The ETV6/RUNX1 fusion gene was the most common genetic alteration (n=16, 17.2%). The most common adverse events during first induction chemotherapy were coagulation abnormalities (n=76, 81.7%), followed by fever (n=71, 76.3%) and alanine transaminase (ALT) elevation (n=34, 36.6%). Compared with negative RAS mutation group, the risk of hyperbilirubinemia was significantly reduced in RAS mutation group (P=0.018), and there was no significant difference in any other adverse events. The average duration of agranulocytosis during first induction chemotherapy was 6 days, and the average duration of agranulocytosis in RAS mutation group and RAS negative group was 6 and 5 days, with no significant difference. Multivariate linear regression analysis showed that in RAS mutation group, when body mass index (BMI) exceeded the median value of this ALL population (BMI >15.38), the risk of agranulocytosis was significantly increased (P=0.003). Conclusions: Newly diagnosed ALL in children with RAS mutation is less likely to be associated with fusion gene expression. RAS mutation increases the risk of agranulocytosis duration during first induction chemotherapy, lowers BMI and reduces the risk of hyperbilirubinemia in ALL children.

Epigenetics and genetics of hepatoblastoma: Linkage and treatment.

Hepatoblastoma is a malignant embryonal tumor with multiple differentiation modes and is the clearest liver malignancy in children. However, little is known about genetic and epigenetic events in Hepatoblastoma. Increased research has recently demonstrated, unique genetic and epigenetic events in Hepatoblastoma, providing insights into its origin and precise treatment. Some genetic disorders and congenital factors are associated with the risk of Hepatoblastoma development, such as the Beckwith-Wiedemann syndrome, Familial Adenomatous polyposis, and Hemihypertrophy. Epigenetic modifications such as DNA modifications, histone modifications, and non-coding RNA regulation are also essential in the development of Hepatoblastoma. Herein, we reviewed genetic and epigenetic events in Hepatoblastoma, focusing on the relationship between these events and cancer susceptibility, tumor growth, and prognosis. By deciphering the genetic and epigenetic associations in Hepatoblastoma, tumor pathogenesis can be clarified, and guide the development of new anti-cancer drugs and prevention strategies.

Synchronization of multi-cluster complex networks.

In this paper, a class of multi-cluster complex networks is discussed. Complete synchronization of such networks is analysed in detail. It is explored how the synchronization depends on the intra coupling matrices, the inter coupling matrices and the corresponding coupling strengths. The approach proposed also applies to more general networks composed of multi-cluster networks, too.

Preoperative QRS Duration Predicts the Responsiveness of Chronic Heart Failure Patients with Pacemaker Indications to Left Bundle Branch Area Pacing Treatment.

BACKGROUND: This study investigated the predictive value of preoperative QRS duration (QRSd) in responsiveness of chronic heart failure (CHF) patients with pacemaker indications to the left bundle branch area pacing (LBBAP). METHODS: Thirty-one CHF patients with cardiac function categorized as NYHA class II or above and indications for pacemaker therapy who successfully underwent LBBAP treatment were enrolled in this study. Based on the 12-month postoperative responsiveness to treatment, patients were divided into a responsiveness group (N = 16) and a no-responsiveness group (N = 15). Data from all patients were collected for analysis. Multivariate binary logistic regression analysis was used to determine the independent factors associated with the responsiveness to LBBAP treatment. RESULTS: Among the 31 patients with LBBAP, 16 patients (51.6%) responded to the treatment, and 15 patients (48.4%) had no response. There were significant differences between the two groups with regard to complete left bundle branch block (CLBBB), preoperative QRSd, and preoperative left ventricular peak time (LVAT). Univariate logistic regression analysis showed that CLBBB, preoperative QRSd, and preoperative LVAT all were significantly correlated with responsiveness to LBBAP. Multivariate binary logistic regression analysis showed that QRSd was an independent predictor of responsiveness to LBBAP. The maximum area under the ROC curve for QRSd was 0.827 (95%C.I.:0.663-0.991), the maximum Youden index was 0.679, with the optimal cutoff point of QRSd ≥ 153 ms, a sensitivity of 81.3%, and a specificity of 86.7%. CONCLUSION: Preoperative QRSd predicts the responsiveness of CHF patients with pacemaker indications to LBBAP.

New effective approach to quasi synchronization of coupled heterogeneous complex networks.

This short paper addresses quasi synchronization of linearly coupled heterogeneous systems. Similarity and difference between the complete synchronization of linearly coupled homogeneous systems and the quasi synchronization of linearly coupled heterogeneous systems will be revealed.

The Implantation of Left Bundle Branch Area Pacing in Patients with and without Bundle Branch Block.

OBJECTIVE: To investigate the clinical safety and electrocardiogram (ECG) characteristics in patients with left bundle branch area pacing (LBBAP). STUDY DESIGN: Retrospective study. PLACE AND DURATION OF STUDY: Department of Cardiology, The First Affiliated Hospital of Bengbu Medical College, Bengbu, China, from May 2018 to January 2020. METHODOLOGY: Patients scheduled for Left Bandle Branch Area Pacing (LBBAP), who were admitted due to bradycardia, had been prospectively recruited. The Medtronic 3830 pacing lead was first placed at the right ventricular (RV) side of the interventricular septum (IVS) with pacing parameters (pacing threshold, pacing impedance and sensing amplitude) and ECG characteristics [QRS morphology, paced QRS duration and stimulus to peak left ventricular activation time (Sti-LVAT)] measured, which was called the right ventricular septum pacing group (RVSP). Then the pacing lead was screwed towards the left ventricular (LV) side of the IVS; and the corresponding parameters and ECG characteristics were assessed, which was called LBBAP group. RESULTS: RVSP caused left bundle block (LBBB) morphology on ECG, while pacing at left bundle area led to right bundle branch block (RBBB) morphology, without remarkable difference in pacing threshold and pacing impedance. The sensing amplitude during LBBAP was significantly higher compared with RVSP (p <0.05). QRS duration and Sti-LVAT were significantly shorter when paced on LBBAP compared with RVSP (p <0.05). Patients with LBBB morphology in intrinsic rhythm showed the greatest reduction in paced QRS duration and Sti-LVAT compared to patients with RBBB morphology or no bundle branch block morphology (p <0.001). There were no complications during pacemaker implantation and no adverse events observed during follow-up. The pacing parameters remained stable during the follow-up (9.2 ± 3.7 months). CONCLUSION: Compared with pacing on RVSP, patients with LBBAP showed RBBB morphology with significantly reduced QRS duration and LV Sti-LVAT under similar pacing parameters. LBBAP is safe and feasible and may be a promising strategy for patients with LBBB morphology who are indicated for ventricular pacing. Key Words: Physiological pacing, Left bundle branch pacing, Right ventricular pacing, Left bundle branch block, Pacemaker.

The effect of Qianliekang tablets on the clinical efficacy, immune function, and inflammatory factor levels in the prostatic fluid of elderly chronic prostatitis patients.

PURPOSE: To study the effect of Qianliekang tablets on the clinical efficacy, immune function, and inflammatory factor levels in the prostatic fluid of elderly chronic prostatitis (CP) patients. METHODS: 106 elderly CP patients admitted to our hospital between June 2018 and June 2020 were recruited as the study cohort and randomly divided into a regular group and an observation group. The regular group was administered tamsulosin hydrochloride, and the observation group was administered a combination of tamsulosin hydrochloride and Qianliekang tablets. After a course of treatment, the clinical efficacy, the changes in the patients' symptoms, the function scores, the prostate ultrasound indicators, the changes in the T lymphocyte subsets, and the inflammatory factor expression levels in the prostatic fluid before and after the treatment were measured and compared in the two groups. The occurrence of adverse effects during the treatment was statistically analyzed. RESULTS: The overall effectiveness rate in the observation group was superior to the overall effectiveness rate in the regular group (94.34% vs. 75.47%, P < 0.05). There were no significant differences in the patient clinical data before the treatment in the two groups (P > 0.05). After the treatment, the CD4 +/CD8 + immune function indicators, the prostatic fluid inflammatory factor levels, the symptom function scores, and the prostate ultrasound indicators in the observation group were better than they were in the regular group (all P < 0.05). No significant differences were found in the incidence of adverse effects between the two groups (P > 0.05). CONCLUSION: Qianliekang tablets can improve the curative effect in elderly CP patients, enhance their immune function, and reduce the inflammatory factor expression levels in their prostatic fluid.

Finite time convergence of pinning synchronization with a single nonlinear controller.

In this paper, we discuss distributive synchronization of complex networks in finite time, with a single nonlinear pinning controller. The results apply to heterogeneous dynamic networks, too. Different from many models, which assume the coupling matrix being symmetric (or the connecting graph is undirected), here, the coupling matrix is asymmetric (or the connecting graph is directed).

CD4-Targeted T Cells Rapidly Induce Remissions in Mice with T Cell Lymphoma.

OBJECTIVE: To explore the immune cell therapy for T cell lymphoma, we developed CD4-specific chimeric antigen receptor- (CAR-) engineered T cells (CD4CART), and the cytotoxic effects of CD4CART cells were determined in vitro and in vivo. METHODS: CD4CART cells were obtained by transduction of lentiviral vector encoding a single-chain antibody fragment (scFv) specific for CD4 antigen, costimulatory factor CD28 fragment, and intracellular signal transduction domain of CD3 fragments. Control T cells were obtained by transduction of reporter lentiviral vector. The cytotoxicity, tumor growth, and survival rate of mice with T cell lymphoma were analyzed after adoptive T cell transfer in vivo. RESULTS: CD4CART cells had potent cytotoxic activity against CD4+ T1301 tumor T cells in a concentration-dependent manner. In addition, adoptive CD4CART cell transfer significantly suppressed tumor growth and improved animal survival with T cell lymphoma, compared to the mice who received control T cells and PBS. CONCLUSION: CD4CART cells have potent cytotoxic effects on T cell lymphoma. The study provided an experimental basis for CD4CART-mediated therapy of T cell lymphoma.

Knockdown of circROBO2 attenuates acute myocardial infarction through regulating the miR-1184/TRADD axis.

BACKGROUND: Studies have found that circular RNAs (circRNAs) play key roles in cardiovascular diseases. However, the function of circROBO2 in acute myocardial infarction (AMI) is unclear. This study aimed to investigate the pathogenesis of circROBO2 in AMI. METHODS: qRT-PCR and Western blot were used to determine the expression levels of circROBO2, miR-1184, and TRADD in AMI and sham-operated mouse models at mRNA and protein level, respectively. The relationship among miR-1184, circROBO2 and TRADD was evaluated by RNA immunoprecipitation (RIP) analysis and luciferase reporter gene analysis. The roles of circROBO2, miR-1184, and TRADD in myocardial cell apoptosis were evaluated using flow cytometry. Ultrasound echocardiography, serum creatine kinase MB (CK-MB) and lactate dehydrogenase (LDH), myocardial infarction area, and myocardial cell apoptosis were measured to examine the effects of circROBO2 on myocardial injury. RESULTS: The expression levels of miR-1184 were significantly reduced, and the expression levels of circROBO2 and TRADD were significantly increased in MI group. CircROBO2 acted as a sponge for miR-1184 by upregulating the expression of TRADD. In addition, overexpression of miR-1184 enhanced the protective effect of knockdown of circROBO2 by partially inhibiting the expression of TRADD in vivo and in vitro. CONCLUSION: Knockdown of circROBO2 reduced the apoptosis of cardiomyocytes by increasing the expression levels of miR-1184, which in turn decreased the expression levels of TRADD in the myocardium post-MI.

QUAD-Condition, Synchronization, Consensus of Multiagents, and Anti-Synchronization of Complex Networks.

In this article, we discuss quadratic condition (QUAD-condition) for general models of synchronization of complex networks and consensus of multiagents with or without pinning controller in detail. Synchronization analysis consists of two parts. One is connection structure, which is described with coupling matrix. The other one is the intrinsic property of the uncoupled system. QUAD-conditions play a key role in describing the intrinsic property of the uncoupled system. With QUAD-conditions, we unify synchronization and consensus of multiagents in a framework. It is interesting that anti-synchronization can be easily transformed to synchronization by introducing suitable QUAD-condition.

A Homozygous Mutation in 5' Untranslated Region of TNFRSF11A Leading to Molecular Diagnosis of Osteopetrosis Coinheritance With Wiskott-Aldrich Syndrome.

Wiskott-Aldrich syndrome (WAS) and osteopetrosis are 2 different, rare hereditary diseases. Here we report clinical and molecular genetics investigations on an infant patient with persistent thrombocytopenia and prolonged fever. He was clinical diagnosed as osteopetrosis according to clinical presentation, radiologic skeletal features, and bone biopsy results. Gene sequencing demonstrated a de novo homozygous mutation in 5'-untranslated region of TNFRSF11A, c.-45A>G, which is relating to osteopetrosis. Meanwhile, a hemizygous transition mutation in WAS gene, c.400G>A diagnosed the infant with WAS. This is the first clinical report for the diagnosis of osteopetrosis coinheritance with WAS in a single patient.

Products of Generalized Stochastic Matrices With Applications to Consensus Analysis in Networks of Multiagents With Delays.

Product theory of stochastic matrices provides a powerful tool in the consensus analysis of discrete-time multiagent systems. However, the classic theory cannot deal with networks with general coupling coefficients involving negative ones, which have been discussed only in very few papers due to the technicalities involved. Motivated by these works, here we developed some new results for the products of matrices which generalize that of the classical stochastic matrices by admitting negative entries. Particularly, we obtained a generalized version of the classic Hajnal inequality on this generalized matrix class. Based on these results, we proved some convergence results for a class of discrete-time consensus algorithms with time-varying delays and general coupling coefficients. At last, these results were applied to the analysis of a class of continuous-time consensus algorithms with discrete-time controller updates in the existence of communication/actuation delays.

Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control.

In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.