Rational Sequence Research Articles

The Journey of Antibody-Drug Conjugates: Lessons Learned from 40 Years of Development.

Antibody-drug conjugates (ADC) represent one of the most rapidly expanding treatment modalities in oncology, with 11 ADCs approved by the FDA and more than 210 currently being tested in clinical trials. Spanning over 40 years, ADC clinical development has enhanced our understanding of the multifaceted mechanisms of action for this class of therapeutics. In this article, we discuss key insights into the toxicity, efficacy, stability, distribution, and fate of ADCs. Furthermore, we highlight ongoing challenges related to their clinical optimization, the development of rational sequencing strategies, and the identification of predictive biomarkers. Significance: The development and utilization of ADCs have allowed for relevant improvements in the prognosis of multiple cancer types. Concomitantly, the rise of ADCs in oncology has produced several challenges, including the prediction of their activity, their utilization in sequence, and minimization of their side effects, that still too often resemble those of the cytotoxic molecule that they carry. In this review, we retrace 40 years of development in the field of ADCs and delve deep into the mechanisms of action of these complex therapeutics and reasons behind the many achievements and failures observed in the field to date.

A System for Countering Possible Threats from the Use of Dangerous Robotic Systems

Based on the generalization and analysis of data from foreign and domestic studies, the article discusses the position that in some cases robotization poses threats proportional to its benefits. The problems and risks caused by the introduction of robotics and their manifestation in various spheres of human activity are outlined. It is noted that the downside of the successful development and use of robotics is the emergence of new types of hazards caused by robots getting out of control or intentionally using them for illegal purposes. The main problems associated with the use of robots are the following: conducting industrial, domestic and other types of espionage, violating traffic safety (air, automobile, marine, etc.), preparing and carrying out terrorist acts, as well as conducting other types of activities dangerous to people and the environment. The structure of the system for countering dangerous robotic complexes for various purposes (RTK VP) and the composition of its main components are proposed, the close relationship of tasks is highlighted, on the one hand, to ensure protection, and on the other, to organize counteraction to RTK VP at the stage of forming tactical and technical requirements for samples of newly created promising robotics products and determining their technical appearance. The analysis of RTK VP as objects of counteraction is given and the main elements of their vulnerability, including the vulnerabilities of groups of robots, are clarified. The probable variants of the illegal use of RTK VP, the causes of their occurrence, the features of their manifestation and the expected consequences are analyzed. The classification of possible ways and means of countering dangerous RTK VP is carried out, and the rational sequence of their implementation is reasoned. A formalized description of the task of countering dangerous RTK VP and a model of the counteraction system are presented. As an indicator of the effectiveness of the counteraction system, it is proposed to use the correspondence of actual and required damage to the object of counteraction in the dynamics of change. Based on the analysis of the features of the counteraction process, a methodological approach to creating a model of a promising anti-RTK VP system is proposed.

START: A Versatile Platform for Bacterial Ligand Sensing with Programmable Performances.

Recognition of signaling molecules for coordinated regulation of target genes is a fundamental process for biological systems. Cells often rely on transcription factors to accomplish these intricate tasks, yet the subtle conformational changes of protein structures, coupled with the complexity of intertwined protein interaction networks, pose challenges for repurposing these for bioengineering applications. This study introduces a novel platform for ligand-responsive gene regulation, termed START (Synthetic Trans-Acting Riboswitch with Triggering RNA). Inspired by the bacterial ligand sensing system, riboswitch, and the synthetic gene regulator, toehold switch, the START platform enables the implementation of synthetic biosensors for various ligands. Rational sequence design with targeted domain optimization yields high-performance STARTs with a dynamic range up to 67.29-fold and a tunable ligand sensitivity, providing a simple and intuitive strategy for sensor engineering. The START platform also exhibits modularity and composability to allow flexible genetic circuit construction, enabling seamless implementation of OR, AND, and NOT Boolean logic gates for multiple ligand inputs. The START design principle is capable of broadening the suite of synthetic biosensors for diverse chemical and protein ligands, providing a novel riboregulator chassis for synthetic biology and bioengineering applications.

ON THE SET OF BETTI ELEMENTS OF A PUISEUX MONOID

Abstract Let M be a Puiseux monoid, that is, a monoid consisting of nonnegative rationals (under standard addition). In this paper, we study factorisations in atomic Puiseux monoids through the lens of their associated Betti graphs. The Betti graph of $b \in M$ is the graph whose vertices are the factorisations of b with edges between factorisations that share at least one atom. If the Betti graph associated to b is disconnected, then we call b a Betti element of M. We explicitly compute the set of Betti elements for a large class of Puiseux monoids (the atomisations of certain infinite sequences of rationals). The process of atomisation is quite useful in studying the arithmetic of Puiseux monoids, and it has been actively considered in recent literature. This leads to an argument that for every positive integer n, there exists an atomic Puiseux monoid with exactly n Betti elements.

Direct prediction of intrinsically disordered protein conformational properties from sequence.

Intrinsically disordered regions (IDRs) are ubiquitous across all domains of life and play a range of functional roles. While folded domains are generally well described by a stable three-dimensional structure, IDRs exist in a collection of interconverting states known as an ensemble. This structural heterogeneity means that IDRs are largely absent from the Protein Data Bank, contributing to a lack of computational approaches to predict ensemble conformational properties from sequence. Here we combine rational sequence design, large-scale molecular simulations and deep learning to develop ALBATROSS, a deep-learning model for predicting ensemble dimensions of IDRs, including the radius of gyration, end-to-end distance, polymer-scaling exponent and ensemble asphericity, directly from sequences at a proteome-wide scale. ALBATROSS is lightweight, easy to use and accessible as both a locally installable software package and a point-and-click-style interface via Google Colab notebooks. We first demonstrate the applicability of our predictors by examining the generalizability of sequence-ensemble relationships in IDRs. Then, we leverage the high-throughput nature of ALBATROSS to characterize the sequence-specific biophysical behavior of IDRs within and between proteomes.

Nontrivial lower bounds for the p-adic valuations of some type of rational numbers and an application for establishing the integrality of some rational sequences

In this note, based on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the p-adic valuation (where p is a given prime number) of some type of rational numbers involving harmonic numbers. Then we use our estimate to derive the integrality of some sequences of rational numbers, which cannot be seen directly from their definitions.

СИНЕРГІЗМ ІНФОРМАЦІЇ АНАЛІЗУ, КОНТРОЛЮ ТА АУДИТУ ДЛЯ ЯКІСНОГО УПРАВЛІННЯ ДІЯЛЬНІСТЮ СУБ’ЄКТА ГОСПОДАРЮВАННЯ

The article highlights the current issues of formation and use of information to ensure effective management of the economic entity. The components of management information support are substantiated. The interrelationship of the information resource, management information support and management information (including result-outcome) is argued, and the order of information data formation according to the proposed structural-logical scheme is systematized. The ways and possibilities of the most optimal implementation of the process of forming information data at the economic entity level according to their types have been identified. This will allow effective and timely processing of information from the internal and external environment in accordance with information needs. It was established that the main elements of ensuring the quality of analytical information are the stages of its analysis in accordance with the task and control over the process of such assessment. The content of the stages of the analysis, its sources and main elements, as well as control over the process of formation and methods of information analysis are substantiated. It is confirmed that the accounting and analytical system of the economic entity in instability should act as the basis for the analysis, control and audit of its activity. This makes it possible to make the most effective management decisions in the short and long term. It is proposed to consider the audit as an element of control over the implementation of management decisions, which enables the improvement of the processes taking place at the economic entity and ensures better efficiency of the flow of all its processes. Attention is focused on the relevance of the introduction of information technologies for analysis and audit. Popular software products and their capabilities in management issues were analysed, the main information threats associated with the use of IT were identified. The components of information protection, which are proposed to be grouped into three groups (managerial, legal and technical protection), are identified, their content and meaning are identified. The imperfection of information protection at modern economic entities is confirmed and it is proposed to include in this system such elements as the identification of threats in the formation and transmission of information, the selection of a software product, determining the method of calculating economic indicators and their grouping, forming a rational sequence in the process of organizing and processing information. This will make it possible to outline the boundaries of information security and control the confidentiality of information use.

Designing E-Course Navigation

In the design of the e-course learning process, it is proposed to use the concept of a navigation model. This model provides convenient and didactically based navigation through the educational material of the course. The work is based on the recent research of the authors on the structuring of educational content in the form of an e-course content model, ordered in the form of a hierarchical structure of the ontologies of learning elements that make up the course. The navigation model concept includes a set of matrices of relations of order and logical coherence of learning elements and corresponding to these matrices of orgraphs of the sequence of study and logical coherence of fragments of educational content. The navigation model answers two important questions of designing an electronic course: 1) what should be the didactically rational sequence of studying the learning elements in the course that is being created; 2) what logical connections should be established between the individual learning elements of the course in order to ensure convenient and didactically based navigation of the course. The mathematical substantiation of the navigation model is given, its properties are investigated, and integral characteristics are introduced. The use of the e-course navigation model helps to: determine and visually represent a rational sequence of studying the educational material, as well as the logical reference links between its various fragments; provide effective assistance to students in navigating the course; analyze and compare different educational materials, assess the level of didactic significance of various learning elements; minimize the complexity of preparing exercises for training and control tests, and the complexity of training and control procedures for e-learning. The concept of a navigation model complies with the international e-learning standards SCORM and IMS, complements them with specific algorithms for aggregating learning objects (SCOs) into e-courses, and assists students in learning them. The mathematical substantiation of the navigation model makes it possible to automate the design of e-courses.

Computer modeling and software research of car and engine parts

Problem. The development of automotive technology for various purposes and the improvement of existing car models, requires a fast and flexible design process. Spatial models of details and nodes are the starting points for design, and the necessary design documentation is performed on their basis. When manufacturing parts on CNC machines, it is necessary to quickly obtain a control program that will increase the accuracy of the product by ensuring the optimal trajectory of the mutual movement of the part and the tool. Therefore, the creation of a comprehensive methodology for the design of car parts, their basic inspection and obtaining design documentation is an important technical task. Goal. The main goal of the work is to determine the rational sequence and basic principles of computer-aided design, research and manufacturing of car and engine parts, and the development of mathematical spatial models of surfaces in order to optimize control programs for CNC machines. Methodology. The approaches adopted in the work for solving the set goal are based on general design principles. The methods of conducting static and dynamic calculations, as well as spatial mathematical modeling of the processes of manufacturing parts were also used. Results. A comprehensive methodology for designing parts of engines and cars has been developed. The main principles of creating spatial models have been determined in order to achieve their flexibility and simple editing. Methods of automating the development of drawings and design documentation are described. The software options for the primary verification of static strength and frequency analysis are considered. A calculation program has been developed for constructing transient and amplitude-phase-frequency characteristics. The mathematical spatial modeling of typical surfaces of the camshaft is provided with the aim of further research and optimization of the development of a control program for processing on a CNC machine tool. Originality. The defined basic principles of designing parts of engines and cars provide an opportunity to create a flexible spatial model and more fully automate the process of drawing up technical documentation. The developed mathematical spatial models of the supporting and working surfaces of the camshaft make it possible to write a control program with the determination of the optimal trajectory of the mutual movement of the part and the tool. Practical value. The obtained results can be recommended when designing car parts and assemblies.

Effect of Microwave Irradiation on the Dielectric Characteristics of Semi-Conductive Nanoparticle-Based Nanofluids: Progress towards the Microwave Synthesis.

Studies on dispersing nanoparticles in base fluid to elevate its essential and critical properties have evolved significantly in the recent decade. Alongside the conventional dispersion techniques used for nanofluid synthesis, microwave energy at 2.4 GHz frequency is irradiated onto the nanofluids is experimented with in this study. The effect of microwave irradiation on the electrical and thermal properties of semi-conductive nanofluids (SNF) is investigated and presented in this article. Titanium dioxide and zinc oxide are the semi-conductive nanoparticles used for this study to synthesize the SNF, viz., titania nanofluid (TNF) and zinc nanofluid (ZNF). Flash and fire points are the thermal properties verified, and dielectric breakdown strength, dielectric constant (εr), and dielectric dissipation factor (tan δ) are the electrical properties verified in this study. AC breakdown voltage (BDV) of TNF and ZNF is improved by 16.78% and 11.25%, respectively, more than SNFs prepared without microwave irradiation. Results justify that the synergetic effect of stirring, sonication, and microwave irradiation in a rational sequence (microwave synthesis) exhibited better electrical and unaltered thermal properties. This microwave-applied nanofluid synthesis could be a simple and effective route to prepare the SNF with improved electrical properties.

Sequencing and combination of current small-molecule inhibitors for chronic lymphocytic leukemia: Where is the evidence?

Small-molecule inhibitors have revolutionized the treatment of chronic lymphocytic leukemia (CLL), a landscape once dominated by chemoimmunotherapy (i.e., an anti-CD20 monoclonal antibody in combination with systemic chemotherapy) in fit and unfit individuals. Key challenges include the management of refractory disease as well as the optimization of the therapy sequence. Decreased responsiveness has been observed with prolonged treatment, especially with Bruton tyrosine kinase (BTK) and phosphatidylinositol 3-kinase (PI3K) inhibitors which are given continuously, while venetoclax, an agent that targets dysregulations in intrinsic apoptosis signaling, has a fixed duration when combined with anti-CD20 monoclonal antibodies or BTK inhibitors. Combination therapy aims to synergistically target different oncogenic signaling pathways to abrogate the proliferation of resistant clones and thereby allows for fixed-duration treatments. An advantage of fixed-duration therapy is the potential to decrease financial and drug-induced toxicities. Sequencing of therapies is important to individualize treatment decisions based on factors such as age, comorbidities, tolerability, and patient preferences. However, to date, there are limited data to guide the rational sequencing or combination of these therapies, since conventional chemoimmunotherapy or chemotherapy regimens were used as comparators against these small-molecule inhibitors in trials that led to their regulatory approvals. In this article, we examined and evaluated the current evidence for sequencing versus the combination of small-molecule inhibitors for CLL by conducting comprehensive searches of the United States National Library of Medicine PubMed database, key meeting abstracts, and clinical practice guidelines. We also summarized findings from expert opinions to elucidate best practices for clinical scenarios with limited evidence to guide treatment selection.

Modeling the sequence of part machining to minimize the time spent on the machining center, considering the working tool changing

An algorithm for choosing a rational sequence for machining a part on a machine with a tool magazine is proposed using the drilling operations example. The algorithm is based on the analysis of all possible options and the calculation of the time spent on each of them. In this respect, the working tool (drill) change is considered, if it is necessary to switch to another machining type (drilling a different diameter hole). Three types of time costs are included in the calculation of the total machining time for one part: the duration of each operation, the duration of the transition to the next operation, and the duration of the working tool change. The result of the algorithm application is the sequence of machining the part with the least total time spent on transitions to the machining areas and the working tool changing.

КОНЦЕПТУАЛЬНИЙ АСПЕКТ ПРИЙНЯТТЯ ДЕРЖАВНОУПРАВЛІНСЬКИХ РІШЕНЬ У СФЕРІ ДЕРЖАВНОЇ БЕЗПЕКИ

In today's conditions of public administration transformation, in accordance with systemic changes in all spheres of social and economic life, the quality of governance and management processes in public authorities in the implementation of development strategies in achieving the goals of management decisions is of particular importance. The main trend of changes in management in public institutions in European countries has been the transfer of management methods and technologies from the commercial sphere to the public sphere. Management approaches and technologies developed in commercial firms are being implemented in the management practice of public organizations: participatory management replaces authoritarian management, and the monopoly on service provision is replaced by competition, competition in service provision, the mechanism of bureaucracy is transformed into the mechanism of the market. At the same time, the transition of management in government agencies from the traditional bureaucratic model to a new management model focused on finding effective solutions to problems is characterized by a greater focus on goals and mission, as opposed to focusing on rules and procedures. The purpose of the study is to form an effective mechanism for making public administration decisions in the field of state security. The article defines the essence of public administration mechanisms for making public administration decisions in the field of state security, namely: legal - in compliance of the decision with the provisions of security legislation, organizational - in establishing a rational sequence of actions of public administration bodies when making an informed decision, structural and functional - in determining the optimal structure of the decision in accordance with the functions and tasks of public administration bodies to ensure state security, which, together with other mechanisms, can be used to make a decision on the basis of the decision. The author summarizes the main elements of a public administration decision, in particular, the plan of action (direction of concentration of the main efforts, sequence and methods of achieving the goal of actions by partial tasks, areas and terms), tasks for security structures, organization of interaction between them, organization of management and support of their actions in crisis conditions.

Addendum to “On the orders of largest groups of automorphisms of compact Riemann surfaces” [J. Pure Appl. Algebra 225 (12) (2021) 106758

Let μ ( g ) be the largest possible order of a group of automorphisms of a compact Riemann surface of genus g ≥ 2 . In the earlier paper we have showed together with Czesław Bagiński that there exist a rational sequence ( r n ) convergent to 8 and infinite sets R n so that μ ( g ) = r n ( g − 1 ) for g ∈ R n . Moreover, assuming the Twin Prime conjecture we have showed the same for 12 i.e. there exist a rational sequence ( s n ) convergent to 12 and infinite sets S n so that μ ( g ) = s n ( g − 1 ) for g ∈ S n . Here we prove the second assertion using Chen theorem instead of relying on TPC.

DETERMINATION OF THE BASIC REQUIREMENTS FOR THE MANAGEMENT SYSTEM OF MILITARY FORMATIONS OF THE NATIONAL GUARD OF UKRAINE DURING THE PERFORMANCE OF COMBAT TASKS, TAKING INTO ACCOUNT THE INFLUENCE OF MODERN MEANS OF ARMED STRUGGLE

The article identifies problems that affect the management system of the military units of the operational assignment of the National Guard of Ukraine during the execution of combat missions in Russia's war with Ukraine. Analysis of the problems of the application of these military units indicates that information and management aspects are considered first during their performance of assigned combat missions. It was established that without determining the most priority requirements for the management system and a rational sequence of measures to achieve them, timely creation and effective functioning is impossible. Analysis of the operating conditions of the management system of military units of operational assignment showed that during the execution of operational tasks, the management process is affected by dynamism and maneuverability of hostilities, the destructive power of high-precision weapons used, the probability of large losses in personnel and equipment, technical equipment of control points, training of officials of control bodies and other factors. The experience of conducting military operations requires early determination of the most important requirements for the management system and a set of measures for the purpose of timely recovery and functioning during the battle (operation).

Algorithms for preliminary assessment of the technical condition of social buildings

The article presents a rational approach to a preliminary assessment of the technical condition of structural elements of social buildings. The authors use the example of kindergartens and schools in the city of Tyumen/ They take into account the date of construction, characteristics of structures and the possibility of choosing effective methods for carrying out repair work. The dependence of the detected damage on the type of structural elements and the building year was revealed. There is also given a rational sequence of actions for assessing the technical condition of building structures with recommendations for their elimination.

Fast Protocols for Characterizing Antibody-Peptide Binding.

Microarray assay formats gained popularity in the 1990s, first implemented in DNA-based arrays but later adopted for use with proteins, namely antibodies, peptides, low molecular weight (LMW) molecules, such as lipids, and even tissues. In nucleic acid-based affinity assays and arrays, but not in protein or peptide arrays, the specificity and affinity of complementary strand interactions can be deduced from or adjusted through modifications to the nucleotide sequence. Arrays of LMW molecules are characterized by largely uniform but low binding affinities. Multiplexed protein-based affinity assays, such as microarrays, might present an additional challenge due to heterogeneity of antigen properties and of their binding affinities. The use of peptides instead of proteins reduces physical heterogeneity of these reagents through either the widened peptide selection options or rational sequence engineering. However, rational engineering of binding affinities remains an unmet need, and peptide-binding affinities to the respective antipeptide antibodies could vary by orders of magnitude. Hence, multiplexing of such assays by using a microarray format and data analysis and interpretation requires some knowledge of their binding affinities. Low-throughput binding assays to characterize such peptide-antipeptide antibodies interactions are widely available, but scaling-up of traditional protein- and peptide-binding assays might present practical challenges. Here, we describe fast label-free practical approach especially suitable for estimating peptide-binding affinities. The method in question relies on commercially available biolayer interferometry-based equipment with a protocol which can be easily scaled-up, subject to user needs and equipment availability.

Development methodology of metrological support of maintenance by the technical state of communication means

Peculiarities of metrological support for technical maintenance based on the condition of large-scale communication devices (tens and hundreds of thousands of elements) consisting of separate subsystems, whose functionality can be checked, maintenance and restoration of functionality can be performed autonomously, are considered. It is suggested to increase the efficiency of technical maintenance according to the condition to take into account the peculiarities of metrological support, to establish a rational sequence of operations, and to reasonably choose measuring equipment depending on the requirements. For this, the methodology uses a complex indicator that combines individual parameters of checks and the probability of their preferred choice. This makes it possible to assess the technical condition of the means of communication in a minimum time with a given probability. In addition, it is possible to quantitatively estimate the time of maintenance, taking into account metrological reliability and the probability of correct assessment of the result of checking parameters by means of measuring equipment. The procedure for using the obtained results is formalized and an example of implementation is given. For the first time, the results of the latest research in the field of technical and metrological support of means of communication during their technical operation are taken into account, namely, the possibility of erroneous assessment of the results of parameter checks, the possibility of failure of measuring equipment, which allows to significantly increase the probability of correct assessment of the technical condition of means of communication during their maintenance according to condition. In addition, taking into account modern achievements in technical diagnostics made it possible to quantitatively estimate the maximum value of the maintenance time based on the state of the means of communication and compare it with the acceptable value specified in the technical documentation. The functional dependencies of the proposed complex coefficient of the feasibility of each inspection, on the metrological reliability of the measuring equipment and the probability of erroneous decisions in the evaluation of the inspection values after measuring the relevant parameters, were obtained and investigated. The area of existence of solutions for calculating the complex coefficient from the quality of metrological support is defined. It is advisable to use the obtained results during the development of the technological process of maintenance of promising and existing means of communication, as well as when planning the activities of specialists during scheduled maintenance work on equipment at field and stationary communication nodes.

МЕТОД ПІДСИЛЕННЯ ЗАЛІЗОБЕТОННИХ МОСТОВИХ ОПОР УЛАШТУВАННЯМ БІТРАПЕЦЕІДАЛЬНОЇ ОБОЙМИ

The paper contains developed the method of reinforcement of reinforced concrete bridge supports by arrangement of reinforced concrete casing on the example of an emergency bridge structure located on the state road M-12 in the Gajsin town, Vinnitsa region. Have been proven that for the further long-term operation of bridge supports, in addition to the reinforcement device, it is also necessary to seal the expansion joints of the span structure located directly above the supports. Have been described the main components of intermediate bridge supports erected in Ukraine during the second half of the 20th century. Have been considered typical defects, which were occurred on the two-cantilever supports of bridge structures during long-term operation. Have been estimated the degree of danger of each of the defects. Have been proved the systemic nature of defects and damages of prefabricated reinforced concrete crossbars.
 Have been considered the probable causes of defects at the bridge supports are considered, namely, destruction of bridges expansion joints. As a result, regular, long-term non-project soaking of supports; violation of the solidity of the concrete protective layer of the working reinforcement of the cantilever parts of the crossbars due its overload; destruction of the mixture from the seams of monolithic semi-crossbars due to its low strength; reinforcement corrosion; loss of frost resistance of concrete; increase in dynamic influences. Have been considered the design and typical defects of standard prefabricated concrete trusses, which are installed on bridge supports for direct perception of loads from the span structure. Have been considered the standard methods of strengthening bridge supports and trusses, their advantages and disadvantages. The paper focuses on the importance and necessity of restoring the tightness of expansion joints by using modern Maurer type constructions in conjunction with the installation of waterproof monolithic or overhead plates of reinforced span structures. Have been proposed an original form of clips for double-console bridge supports in the form of double-trapezoids which significantly improve their architectural expressiveness and optimize the structural scheme of supports. Have been proposed to use self-compressing concrete to save material costs and time during the construction of temporary special and auxiliary devices (formwork) for monolithic casing. Have been proposed an effective methodology and a rational technological sequence for performing work on strengthening.
 Have been summarized the practical experience of performing construction and installation works on monolithic supports with self-compacting concrete mixes according to the method proposed by the authors of the article which were made according to the technology of Sika. Have been summarized the experience of bridge operation after sealing expansion joints and overhaul of bridge supports.

On radiuses of convergence of q-metallic numbers and related q-rational numbers

The q-rational numbers and the q-irrational numbers are introduced by S. Morier-Genoud and V. Ovsienko. In this paper, we focus on q-real quadratic irrational numbers, especially q-metallic numbers and q-rational sequences which converge to q-metallic numbers, and consider the radiuses of convergence of them when we assume that q is a complex number. We construct two sequences given by recurrence formula as a generalization of the q-deformation of Fibonacci numbers and Pell numbers which are introduced by S. Morier-Genoud and V. Ovsienko. We give an estimation of radiuses of convergence of them, and we solve on conjecture of the lower bound expected which is introduced by L. Leclere, S. Morier-Genoud, V. Ovsienko, and A. Veselov for the metallic numbers and its convergence rational sequence. In addition, we obtain a relationship between the radius of convergence of the [n,n,...,n,...]_q and [n,n,...,n]_q in the case of n=3 and n=4.