Rational Sequence Research Articles

Expert Formation of Functional Parameters Composition in Digital Mechatronic Systems

In the process of the mechatronic system functioning respective effective output parameters and parameters of its internal system state are generated. Preliminary selection of composition of the indicated parameters is a rather complicated task due to objective complexity of systems, availability of evident and latent interrelations between parameters. This task is complicated due to the necessity of simultaneous reduction of dimension and variation of control procedures and management in the mechatronic system. Solution of this problem may be attained with the aid of preliminary expert and empirical studies of complex models and mock-up specimens of designed mechatronic systems. In this regard, this work contains presentation of methodological aspects of adequately supported formation of composition of controlled parameters, their tolerance limits and other system features required for intellectual management. Rational sequence is described for performance of focused researches in order to reveal most important effective output parameters and parameters of internal system states. In accordance with the proposed algorithm the initial information and parameter picture of the intelligent mechatronic system is formed, studied and revised, its group expert evaluation and subsequent "thinning-out" of lists of its constituent parameters. A regression model is developed, which determines the form of interrelation between the parameters, as well as of the correlation model, which allows assessment of the volume of statistical interrelation between the system parameters. In the process of model analysis extremely weak dependences are detected between parameters, negative collinearity of factor variables is eliminated.

On the Laxton group

In 1969, Laxton defined a multiplicative group structure on the set of rational sequences satisfying a fixed linear recurrence of degree two. He also defined some natural subgroups of the group, and determined the structures of their quotient groups. Nothing has been known about the structure of Laxton’s whole group and its interpretation. In this paper, we redefine his group in a natural way and determine the structure of the whole group, which clarifies Laxton’s results on the quotient groups. This definition makes it possible to use the group to show various properties of such sequences.

Substantiation of the rational sequence of processes of aerosol gradient technologies in elements of ship power plants

Substantiation of the rational sequence of processes of aerosol gradient technologies in elements of ship power plants

Diagnosis of electronic engine control systems for LADA automobile

The article is devoted to the development of a system for ensuring the efficiency of ECM through the introduction of diagnostics of its technical condition into the technological processes of servicing and repairing vehicles. In order to create such a system, we performed studies on the operational reliability of the structural elements of the ECU, the effect of their failures on the engine operating parameters, and the substantiation of diagnostic parameters evaluating the technical condition of the system. The object of the research is the electronic control system M86, installed on domestic LADA VESTA automobiles (VAZ-21179 engine). According to the results of the research, the average operating time of the structural elements of the ECM to failure and the reasons for their occurrence were established. Authors imitated the failure of each ECM elements by turning it off and using the appropriate equipment to measure selected parameters of engine operation. The most significant influence on the operation of the engine is caused by failure of fuel pump, ECU and crankshaft position sensor. The failure of this elements causes the complete loss of engine performance as fuel supply to the cylinders stops. In case of failure of other elements of ECM the engine performance is maintained, but its operating capabilities significantly decrease. To ensure the required level of reliability of the ECM, it is necessary at regular intervals to maintain the vehicles to diagnose the technical condition of its elements at automobile service enterprises. In this paper, it is recommended to split the ECM into three subsystems, each of which is evaluated by one complex diagnostic parameter reflecting the technical condition of the structural elements included there. The deviation of the parameters beyond the tolerance limits caused by the occurrence of faults serves as the basis for deciding whether to conduct the necessary technical actions. Diagnostics of the ECM subsystems is carried out in accordance with the developed algorithms that establish a rational sequence of control, adjustment and other operations to identify and eliminate damages arising in the process of operation. As an example, the article presents an algorithm for diagnosing the fuel supply subsystem and reducing the toxicity of exhaust gases. The developments proposed in the article were tested and introduced into the technological processes of maintenance and automobile repairs of the LADA dealership center in the city of Vladimir.

Approximations of Algebraic Irrationalities with Matrices

We discuss the use of matrices for providing sequences of rationals that approximate algebraic irrationalities. In particular, we study the regular representation of algebraic extensions, proving that ratios between two entries of the matrix of the regular representation converge to specific algebraic irrationalities. As an interesting special case, we focus on cubic irrationalities giving a generalization of the Khovanskii matrices for approximating cubic irrationalities. We discuss the quality of such approximations considering both rate of convergence and size of denominators. Moreover, we briefly perform a numerical comparison with well-known iterative methods (such as Newton and Halley ones), showing that the approximations provided by regular representations appear more accurate for the same size of the denominator.

METHOD OF LOGICAL SCHEMES OF SUBJECT CONTENT FOR QUALITY ASSURANCE OF DEVELOPED INTERACTIVE ELECTRONIC TECHNICAL MANUALS

The determining value of the logicality of the presentation, relevance and visibility of the presentation of the subject content to ensure the quality of the developed interactive electronic technical manuals for the operation and repair of aviation equipment objectively requires the development of a methodological tool for monitoring and managing its consumer properties. As such, the method of logical schemes of subject content for technical systems, which are built on the basis of synthesis of recognition features, can serve. These schemes are a network description of the multilevel decomposition of complex samples of aviation technical systems in a rational sequence of their inspection, verification and development. The proposed method of ensuring the quality of the IET develops a qualitatively new level of development of the subject material for the operation and repair of aviation equipment for interactive electronic manuals by supplementing the scientific and methodological apparatus of such development with tools for its generalization and structuring as logical diagrams of the sequence of inspections (work).The method of logical schemes of subject content to ensure the quality of interactive electronic technical guides being developed includes: a method for synthesizing logical diagrams of the subject content of operation and repair of aviation equipment, the basic sequence of the stages of developing electronic content on the basis of logical diagrams of subject content; practical recommendations on the software implementation of electronic content in interactive electronic technical guides.

Impact of the integration of lupine (Lupinus albus) into crop rotation on the extent of soil compaction in the Westsik longterm field trial

In order to reduce or eliminate soil compaction, rational crop rotation and appropriate sequence of crops have an increasingly important role in addition to mechanical and tillage solutions. In this respect, introduction of greening in recent years has been a major step, which focuses on aspects of environmentally conscious, soil conserving farming and the improvement of biodiversity. The cornerstone of this strategy is the cultivation of crops that have a beneficial effect on soil properties, such as the use of nitrogen-fixing plants and green manure plants in the cultivation system that have a beneficial effect on soil structure. In our examinations, penetrometer measurements were carried out in the second longest crop rotation-based field experiment in Europe in order to quantify the effects of green crops and crop rotation strategies on soil resistance. Our aim was to evaluate and compare the impact of lupine (Lupinus albus) on the penetration resistance of soil on sour sandy soils. At the time of the penetration resistance measurement, different crop rotations had a significant effect on the development of the parameter in the examined soil layer. The most favourable penetration resistance values were found in the crop rotation, which included lupine as a green manure. The favourable effect is dominant below the cultivated layer (0–40 cm), which is statistically verified. The values of penetration resistance of the cultivated soil layer of lupine sown as primary green manure did not differ significantly from the values measured in the case of the fallowing-based crop rotation. Therefore, the use of lupine green manure instead of fallowing could be worth considering by practical application due to its favourable effects on soil penetration resistance. The use of lupine green manure after the production of rye cultivation resulted in penetration parameters similar to fallowing, irrespective of the green crop and the applied amount of nitrogen fertilizer, which justifies the cultivation of the crop as green manure. In the case of potato cultivating, recorded compaction within the cultivated layer is an obvious consequence of mechanical compaction during harvest; therefore, machinery operations are decisive for the development of penetration resistance values of the cultivated layer. In addition to the beneficial effect of lupine as a green manure crop on soil condition, its nitrogen-fixing ability is also important; it stresses the utilisation of the crop of sour sandy soils for the sake of proper soil management.

Forming a defective surface layer when cutting parts made from carbon-carbon and carbon-polymeric composites

We report results of theoretical and experimental research aimed at establishing the mechanisms for the formation of a defective layer at the machined surfaces made from carbon composite materials, specifically those from carbon-carbon and carbon-polymeric groups. Possessing a set of unique physical and mechanical properties, the latter are increasingly applied in aviation and space technologies. However, since the properties of a material are predetermined not only by the components applied but also by the processes to obtain products (laying of reinforcing fibers, orientation of threads), conducting mechanical tests of samples-witnesses is a compulsory stage in the operations performed. Based on the generalization of statistical and theoretical-analytical information, we have developed a model of the emergence and propagation of cracks in a quasi-fragile material, particularly the carbon-carbon and carbon-polymeric composites, caused by the action of a cutting wedge. It is shown that the stresses that occur in a surface layer predetermine the intensity of crack growth while a direction of microcracks propagation is due to the applied force load. Therefore, control over the direction of force action, as well as the application of certain technical means, including a hydroabrasive jet, could enable the localization of microcracks in small quantities at the surface of the formed edge. The established regularities in the formation of a defective layer at machining (including the hydroabrasive cutting) have made it possible to identify ways to improve the quality of a sample and to reduce the layer thickness to 0.05 mm. The derived dependences of the destruction zone parameters on the stresses that occur at cutting allowed us to obtain the rational sequence of machining transitions, at which the defective surface layer is the smallest. The results obtained provide a possibility to significantly increase the accuracy of mechanical tests of carbon composite materials, thereby reducing the variance in the measurements of controlled parameters by 30‒40 %. The results have been actually implemented industrailly, and are of interest for the further research aimed at the hybridization of processes, as well as the development of technologies based on a functional-oriented approach.

Functional Approach to Development of Hybrid Technology of Cutting Diamond Carbides

Background: Modern composite materials have a number of advantages in comparison with the traditionally used ones and allow implementing new methods of processing, which makes the finished product cheaper and makes its use more efficient.Objective: In order to improving the surface quality and productivity taken by A functional approach. Method: A functional approach to the development of cutting technologies for Carbide and Super Hard Multilayered Composites is considered. It allows, by alternating the effects of different nature, to obtain qualitative edges, to lower the residual stresses in the surface layers, and to achieve a high surface quality. The essence of the approach is that the method of impact is determined on the basis of a morphological search of options for the execution of individual surface elements, each of which, combined into a set, uniquely forms the function of the finished product. The cutting is determined by a rational sequence of execution of technological transitions, provided that each harmful intermediate function at the finish stage turns into neutral or complements the required useful function.Results: Examples of figured cutting of plates from polycrystalline diamond-containing materials are given, the results of obtaining qualitative edges are shown.Conclusion: Thanks to the proposed technology based on the use of a functionally oriented approach, the functions of the tool for cutting are divided between the tool itself and the product part. As a result, the processing speed increases more than 3 times, and a high cut quality is achieved.

Functional Approach to Development of Hybrid Technology of Cutting Diamond Carbides

Background: Modern composite materials have a number of advantages in comparison with the traditionally used ones and allow implementing new methods of processing, which makes the finished product cheaper and makes its use more efficient.Objective: In order to improving the surface quality and productivity taken by A functional approach. Method: A functional approach to the development of cutting technologies for Carbide and Super Hard Multilayered Composites is considered. It allows, by alternating the effects of different nature, to obtain qualitative edges, to lower the residual stresses in the surface layers, and to achieve a high surface quality. The essence of the approach is that the method of impact is determined on the basis of a morphological search of options for the execution of individual surface elements, each of which, combined into a set, uniquely forms the function of the finished product. The cutting is determined by a rational sequence of execution of technological transitions, provided that each harmful intermediate function at the finish stage turns into neutral or complements the required useful function.Results: Examples of figured cutting of plates from polycrystalline diamond-containing materials are given, the results of obtaining qualitative edges are shown.Conclusion: Thanks to the proposed technology based on the use of a functionally oriented approach, the functions of the tool for cutting are divided between the tool itself and the product part. As a result, the processing speed increases more than 3 times, and a high cut quality is achieved.

The method of rational dispatching a sequence of heterogeneous repair works

For critically important power systems, some repair works should be performed by one repair brigade at the same time. Conditions for performing different works are often characterized by uncertainties. In practice, the term is given for each work, and possible damages exist if the performance of works is not well-timed. Taking into account these factors, the sequence of performing heterogeneous repair works essentially influences the safety and/or efficiency of the power system. The method of rational dispatching of the sequence of heterogeneous repair works considering the requirements of timeliness for their performance is proposed in this paper. The rational sequence of works is established by criteria of minimizing integral damages based on the best choices from different dispatcher technologies and their parameters (such as distribution of work call types by priorities, distribution of call priorities into groups, appointment of technologies inside groups). A possible effect is demonstrated by an example.

Integrated Molecular Analysis Identifies Replicative Stress As Sensitizer to Imetelstat Therapy in AML

Telomerase activation enables replicative immortality in the majority of cancers including acute myeloid leukemia (AML). Imetelstat competitively inhibits telomerase activity with recently reported clinical efficacy in myelodysplasia and myelofibrosis. Here we show final results on a randomized preclinical trial in AML patient-derived xenografts (PDX; n = 30 individual AML; each treated with imetelstat vs. vehicle control; n = 6 per condition). Using drug sensitivity scores (DSS) to define in vivo PDX responses, we provide integrated phenotypic, cytogenetic, genomic and transcriptomic analysis of samples to understand AML response to imetelstat. We use this mechanistic insight to rationally sequence induction chemotherapy with imetelstat to optimize in vivo responses, even in initially poorly responding samples.Methods: An AML PDX cohort was established using bone marrow (BM) or peripheral blood (PB) samples collected from 30 AML patients and transplanted into NOD/SCID/IL2gR-/-/hIL3,CSF2,KITLG (NSGS; n = 12 recipients / AML patient sample). AML onset was defined by reconstitution of BM and spleen with CD45+ CD33+ donor cells, circulating blasts, anemia (HCT < 35%) or thrombocytopenia (PLT < 400 x 10^6/ml). After initial engraftment was confirmed by PB chimerism (> 1%), recipients were treated with imetelstat (15 mg/kg I.P.) or control every 48 - 72h.Results: Across the entire cohort, survival was improved for imetelstat- vs. PBS-treated PDX (Median survival PBS: 88d, Imetelstat: 138d; Hazard ratio PBS: 2.87; 2.20 to 3.74; Cox proportional hazards model: p < 0.0001), however there were clear differences in the quality and duration of response to imetelstat treatment. In order to quantify the sensitivity of each individual AML patient sample to therapy, DSS were derived using the area under the curve of PB donor chimerism in PBS versus imetelstat-treated recipients (Mean DSS entire cohort: 3.21 ± 0.36). DSS positively correlated with survival benefit (R square: 0.87), and values higher than 2.3 gained at least 30 days of survival benefit. Based on DSS, AML patient samples were grouped into “Sustained” (17 AML patient samples; 57%) or “Poor” responders (13 AML patient samples; 43%) with DSS 2.3 as cut-off value. European LeukemiaNet 2017 adverse prognostic samples were trend-wise enriched in poor vs. sustained responders to imetelstat (83.3% poor vs. 16.7% sustained response; p = 0.06, Fisher's exact test). RNA sequencing and mutational profiling was performed on all baseline AML samples. Differential expression analysis revealed a gene signature specifically expressed in sustained compared to poor responders (p < 0.05; log2FC > 1.5; 109 annotated genes) that was functionally annotated in replicative stress including nucleosome (p = 0.01), transcription factor activity (p = 0.04), and sequence-specific DNA binding (p = 0.04).We therefore examined whether the induction of replicative stress could sensitize response to imetelstat therapy. Seven independent AML patient samples with poor response to imetelstat monotherapy were transplanted into NOD.Rag1-/-Il2Rg-/-/ hIL3,CSF2,KITLG (NRGS). Mice received standard induction chemotherapy intravenously as a cytarabine (Arac; 50 mg/kg) and doxorubicin (Doxo; 1.5 mg/kg) 5+3 dosing regimen followed by continuous imetelstat therapy vs. imetelstat alone, standard induction chemotherapy alone, or vehicle control (n = 6 / group, n = 24 / AML sample). Combination therapy significantly prolonged overall survival (Median survival: Control: 38.5d; Imetelstat: 41d; Arac+Doxo: 61d; Arac+Doxo + Imetelstat: 71d post-start of treatment; Hazard ratio Arac+Doxo alone vs. Arac+Doxo+Imetelstat: 2.34; 1.19 to 4.586; Cox proportional hazards model: p < 0.001).In summary, imetelstat prolonged overall survival in a large cohort of AML PDX. In 57% (17 out of 30 individual AML patient samples), sustained responses to imetelstat were associated with marked improvements in survival and a baseline replicative stress-annotated transcriptional signature. The rational sequencing of standard induction chemotherapy to induce replicative stress provides proof-of-concept to sensitize imetelstat-resistant AML patient samples and suppress expansion and prevent relapse in AML. DisclosuresLane:novartis: Consultancy; janssen: Consultancy, Research Funding.

Enhancing Vaccine Efficacy by Engineering a Complex Synthetic Peptide To Become a Super Immunogen.

Peptides offer enormous promise as vaccines to prevent and protect against many infectious and noninfectious diseases. However, to date, limited vaccine efficacy has been reported and none have been licensed for human use. Innovative ways to enhance their immunogenicity are being tested, but rational sequence modification as a means to improve immune responsiveness has been neglected. Our objective was to establish a two-step generic protocol to modify defined amino acids of a helical peptide epitope to create a superior immunogen. Peptide variants of p145, a conserved helical peptide epitope from the M protein of Streptococcus pyogenes, were designed by exchanging one amino acid at a time, without altering their α-helical structure, which is required for correct antigenicity. The immunogenicities of new peptides were assessed in outbred mice. Vaccine efficacy was assessed in a skin challenge and invasive disease model. Out of 86 variants of p145, seven amino acid substitutions were selected and made the basis of the design for 18 new peptides. Of these, 13 were more immunogenic than p145; 7 induced Abs with significantly higher affinity for p145 than Abs induced by p145 itself; and 1 peptide induced more than 10,000-fold greater protection following challenge than the parent peptide. This peptide also only required a single immunization (compared with three immunizations with the parent peptide) to induce complete protection against invasive streptococcal disease. This study defines a strategy to rationally improve the immunogenicity of peptides and will have broad applicability to the development of vaccines for infectious and noninfectious diseases.

Clinical Practice Guideline: Evaluation of the Neck Mass in Adults.

ObjectiveNeck masses are common in adults, but often the underlying etiology is not easily identifiable. While infections cause most of the neck masses in children, most persistent neck masses in adults are neoplasms. Malignant neoplasms far exceed any other etiology of adult neck mass. Importantly, an asymptomatic neck mass may be the initial or only clinically apparent manifestation of head and neck cancer, such as squamous cell carcinoma (HNSCC), lymphoma, thyroid, or salivary gland cancer. Evidence suggests that a neck mass in the adult patient should be considered malignant until proven otherwise. Timely diagnosis of a neck mass due to metastatic HNSCC is paramount because delayed diagnosis directly affects tumor stage and worsens prognosis. Unfortunately, despite substantial advances in testing modalities over the last few decades, diagnostic delays are common. Currently, there is only 1 evidence-based clinical practice guideline to assist clinicians in evaluating an adult with a neck mass. Addition...

Self-assembly nanostructure controlled sustained release, activity and stability of peptide drugs

Peptides are considered as a new generation of drugs due to their high structural and functional diversity. However, the development of peptide drugs is always limited by their poor stability and short circulation time. Carriers are applied for peptide drug delivery, but there may be problems like poor loading efficiency and undesired xenobiotic toxicity. Peptide self-assembly is an effective approach to improve the stability and control the release of peptide drugs. In this study, two self-assembling anticancer peptides are designed by appending a pair of glutamic acid and asparagine to either the N-terminus or the C-terminus of a lytic peptide. This simple, yet rational sequence modification was made to change the amphiphilic pattern and secondary structural content of the parent peptide, thereby modulating its self-assembly process. It was found that the N-terminus modified peptide favors the formation of nanofibrils and the peptide with C-terminal modification formed micelles. Although both nanostructures showed prolonged action profiles and improved serum stability compared to the parent peptide, the morphology of the nanostructures is highly critical to manipulate the release profile of the free peptide from the assembly and regulate their bioactivity. We believe the self-assembly approach demonstrated in this study can be applied to a variety of therapeutic peptide drugs to improve their stability and therapeutic activity for the development of carrier-free drug delivery system.

New insights into a classic aptamer: binding sites, cooperativity and more sensitive adenosine detection.

The DNA aptamer for adenosine (also for AMP and ATP) is a highly conserved sequence that has recurred in a few selections. It it a widely used model aptamer for biosensor development, and its nuclear magnetic resonance structure shows that each aptamer binds two AMP molecules. In this work, each binding site was individually removed by rational sequence design, while the remaining site still retained a similar binding affinity and specificity as confirmed by isothermal titration calorimetry. The thermodynamic parameters of binding are presented, and its biochemical implications are discussed. The number of binding sites can also be increased, and up to four sites are introduced in a single DNA sequence. Finally, the different sequences are made into fluorescent biosensors based on the structure-switching signaling aptamer design. The one-site aptamer has 3.8-fold higher sensitivity at lower adenosine concentration with a limit of detection of 9.1 μM adenosine, but weaker fluorescence signal at higher adenosine concentrations, consistent with a moderate cooperativity in the original aptamer. This work has offered insights into a classic aptamer for the relationship between the number of binding sites and sensitivity, and a shorter aptamer for improved biosensor design.

Discovering Novel Antimicrobial Peptides using High-Throughput Screening in the Presence of Human Erythrocytes

Antimicrobial peptides (AMPs) have long been considered excellent candidates for development as antibiotic agents to combat the threat of drug resistant bacterial pathogens. Yet, the promise AMPs have displayed in the laboratory has not yielded correlative clinical success. We hypothesized that a major reason for the disparity between outcomes at the bench and in the clinic is AMP interaction with and toxicity towards host cells. Here, we validate this theory using human red blood cells as model eukaryotic cells. Indeed, the potency of several well-studied antimicrobial peptides decreases from minimum sterilizing concentrations (MSC) of 1-5 μM to >30 μM in the presence of RBCs at 1x109 cells/ml; equivalent to 20% of the human physiological concentration. To address this issue, we have developed a high-throughput method to screen a combinatorial peptide library for antimicrobial activity in the presence of concentrated human cells. The screen consists of assays that assess the effect of RBCs on antimicrobial activity as well as toxicity toward eukaryotic cells. We present data on peptides identified and characterized from the high-throughput library screen and show that these new peptides were not as effective as they initially appeared during the screen. We demonstrate that the difference between observed and expected results is due to unforeseen proteolytic activity sequestered within the cytosol of the red blood cells. Finally, we show that a library consensus sequence synthesized using all d-amino acids outperforms all library isolates as well as the template sequence in terms of microbicidal activity in the presence of RBCs. Ultimately, our results suggest that combining the power of combinatorial library screening with the nuance of rational sequence engineering is an effective approach to engineering novel antimicrobial peptides that retain activity under physiological conditions.

Finiteness and rational sequences, constructively

AbstractRational sequences are possibly infinite sequences with a finite number of distinct suffixes. In this paper, we present different implementations of rational sequences in Martin–Löf type theory. First, we literally translate the above definition of rational sequence into the language of type theory, i.e., we construct predicates on possibly infinite sequences expressing the finiteness of the set of suffixes. In type theory, there exist several inequivalent notions of finiteness. We consider two of them, listability and Noetherianness, and show that in the implementation of rational sequences the two notions are interchangeable. Then we introduce the type of lists with backpointers, which is an inductive implementation of rational sequences. Lists with backpointers can be unwound into rational sequences, and rational sequences can be truncated into lists with backpointers. As an example, we see how to convert the fractional representation of a rational number into its decimal representation and vice versa.

HARMONIC ANALYSIS ON THE POSITIVE RATIONALS. DETERMINATION OF THE GROUP GENERATED BY THE RATIOS

The multiplicative group generated by a certain sequence of rationals is determined, settling a 30-year conjecture.

On Higher-Dimensional Fibonacci Numbers, Chebyshev Polynomials and Sequences of Vector Convergents

We study higher-dimensional interlacing Fibonacci sequen\-ces, generated via both Chebyshev type functions and $m$-dimensional recurrence relations. For each integer $m$, there exist both rational and integer versions of these sequences, where the underlying prime congruence structures of the rational sequence denominators enables the integer sequence to be recovered. From either the rational or the integer sequences we construct sequences of vectors in $\mathbb{Q}^m$, which converge to irrational algebraic points in $\mathbb{R}^m$. The rational sequence terms can be expressed as simple recurrences, trigonometric sums, binomial polynomials, sums of squares, and as sums over ratios of powers of the signed diagonals of the regular unit $n$-gon. These sequences also exhibit a ``rainbow type'' quality, and correspond to the Fleck numbers at negative indices, leading to some combinatorial identities involving binomial coefficients. It is shown that the families of orthogonal generating polynomials defining the recurrence relations employed, are divisible by the minimal polynomials of certain algebraic numbers, and the three-term recurrences and differential equations for these polynomials are derived. Further results relating to the Christoffel-Darboux formula, Rodrigues' formula and raising and lowering operators are also discussed. Moreover, it is shown that the Mellin transforms of these polynomials satisfy a functional equation of the form $p_n(s)=\pm p_n(1-s)$, and have zeros only on the critical line $\Re (s)=1/2$.