On a new family of gauss k-Lucas numbers and their polynomials

2020 ◽  
pp. 2150101
Author(s):  
Engi̇n Özkan ◽  
Merve Taştan
Keyword(s):  
Matrix Representation ◽  
Lucas Numbers ◽  
Generalized Polynomials ◽  
Lucas Polynomials ◽  
New Family ◽  
The Family

In this paper, we define a new family of Gauss [Formula: see text]-Lucas numbers. We give the relationships between the family of the Gauss [Formula: see text]-Lucas numbers and the known Gauss Lucas numbers. We also define the generalized polynomials for these numbers. We obtain some interesting properties of the polynomials. We also give the relationships between the generalized Gauss [Formula: see text]-Lucas polynomials and the known Gauss Lucas polynomials. Furthermore, we find new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini’s identities for the families and their polynomials.

scholarly journals A NEW FAMILIES OF GAUSS k-JACOBSTHAL NUMBERS AND GAUSS k-JACOBSTHAL-LUCAS NUMBERS AND THEIR POLYNOMIALS

2020 ◽  
Vol 20 (4) ◽  
pp. 893-908
Author(s):  
ENGİN ÖZKAN ◽  
MERVE TAŞTAN
Keyword(s):  
Matrix Representation ◽  
Lucas Numbers ◽  
Generalized Polynomials ◽  
Lucas Polynomials ◽  
The Family

In this paper, we define the new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers. We obtain some exciting properties of the families. We give the relationships between the family of the Gauss k-Jacobsthal numbers and the known Gauss Jacobsthal numbers, the family of the Gauss k-Jacobsthal-Lucas numbers and the known Gauss Jacobsthal-Lucas numbers. We also define the generalized polynomials for these numbers. Further, we obtain some interesting properties of the polynomials. In addition, we give the relationships between the generalized Gauss k-Jacobsthal polynomials and the known Gauss Jacobsthal polynomials, the generalized Gauss k-Jacobsthal-Lucas polynomials and the known Gauss Jacobsthal-Lucas polynomials. Furthermore, we find the new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini’s Identities for the families and their polynomials.

scholarly journals The generalized k-Fibonacci polynomials and generalized k-Lucas polynomials

2021 ◽  
Vol 27 (2) ◽  
pp. 148-158
Author(s):  
Merve Taştan ◽  
◽  
Engin Özkan ◽  
Anthony G. Shannon ◽  
◽  
...  
Keyword(s):  
Matrix Representation ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
The Family ◽  
Generalized Lucas Polynomials

In this paper, we define new families of Generalized Fibonacci polynomials and Generalized Lucas polynomials and develop some elegant properties of these families. We also find the relationships between the family of the generalized k-Fibonacci polynomials and the known generalized Fibonacci polynomials. Furthermore, we find new generalizations of these families and the polynomials in matrix representation. Then we establish Cassini’s Identities for the families and their polynomials. Finally, we suggest avenues for further research.

scholarly journals Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3361-3368
Author(s):  
Abbas Wanas
Keyword(s):  
Univalent Functions ◽  
Lucas Polynomials ◽  
New Family ◽  
The Family

In this article, we use the (M,N)-Lucas polynomials to define a new family H?(?,x) of normalized holomorphic and bi-univalent functions and to establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we investigate Fekete-Szeg? inequality for functions in the family H?(?,x) which we have introduced here.

Three new species, two new genera, and new family Biphragmosagittidae (Сhaetognatha) from Southwest Pacific Ocean

2011 ◽  
Vol 20 (1) ◽  
pp. 161-173
Author(s):  
A.P. Kassatkina
Keyword(s):  
New Species ◽  
Type Species ◽  
Morphological Characters ◽  
The Body ◽  
New Order ◽  
New Genera ◽  
New Family ◽  
The Family ◽  
Three New Species

Resuming published and own data, a revision of classification of Chaetognatha is presented. The family Sagittidae Claus & Grobben, 1905 is given a rank of subclass, Sagittiones, characterised, in particular, by the presence of two pairs of sac-like gelatinous structures or two pairs of fins. Besides the order Aphragmophora Tokioka, 1965, it contains the new order Biphragmosagittiformes ord. nov., which is a unique group of Chaetognatha with an unusual combination of morphological characters: the transverse muscles present in both the trunk and the tail sections of the body; the seminal vesicles simple, without internal complex compartments; the presence of two pairs of lateral fins. The only family assigned to the new order, Biphragmosagittidae fam. nov., contains two genera. Diagnoses of the two new genera, Biphragmosagitta gen. nov. (type species B. tarasovi sp. nov. and B. angusticephala sp. nov.) and Biphragmofastigata gen. nov. (type species B. fastigata sp. nov.), detailed descriptions and pictures of the three new species are presented.

Correcting a 135-year error: Limulidae Leach, 1819 (Chelicerata, Xiphosura) is the proper authority, not Limulidae Zittel, 1885

2021 ◽  
pp. 1-2
Author(s):  
Philip M. Novack-Gottshall ◽  
Roy E. Plotnick
Keyword(s):  
Horseshoe Crab ◽  
Marine Species ◽  
Limulus Polyphemus ◽  
Junior Synonym ◽  
Living Fossil ◽  
New Family ◽  
The Family ◽  
The World ◽  
Modern Genus

The horseshoe crab Limulus polyphemus (Linnaeus, 1758) is a famous species, renowned as a ‘living fossil’ (Owen, 1873; Barthel, 1974; Kin and Błażejowski, 2014) for its apparently little-changed morphology for many millions of years. The genus Limulus Müller, 1785 was used by Leach (1819, p. 536) as the basis of a new family Limulidae and synonymized it with Polyphemus Lamarck, 1801 (Lamarck's proposed but later unaccepted replacement for Limulus, as discussed by Van der Hoeven, 1838, p. 8) and Xyphotheca Gronovius, 1764 (later changed to Xiphosura Gronovius, 1764, another junior synonym of Limulus). He also included the valid modern genus Tachypleus Leach, 1819 in the family. The primary authority of Leach (1819) is widely recognized in the neontological literature (e.g., Dunlop et al., 2012; Smith et al., 2017). It is also the authority recognized in the World Register of Marine Species (WoRMS Editorial Board, 2021).

Early Paleozoic Hyolitha from North America: reexamination of Walcott's and Resser's type specimens

1988 ◽  
Vol 62 (2) ◽  
pp. 218-233 ◽  
Author(s):  
John Mark Malinky
Keyword(s):  
North America ◽  
Lower Cambrian ◽  
Type Species ◽  
New Genus ◽  
Early Paleozoic ◽  
Type Specimens ◽  
Middle Cambrian ◽  
Upper Cambrian ◽  
New Family ◽  
The Family

Concepts of the family Hyolithidae Nicholson fide Fisher and the genera Hyolithes Eichwald and Orthotheca Novak have been expanded through time to encompass a variety of morphologically dissimilar shells. The Hyolithidae is here considered to include only those hyolithid species which have a rounded (convex) dorsum; slopes on the dorsum are inflated, and the venter may be flat or slightly inflated. Hyolithes encompasses species which possess a low dorsum and a prominent longitudinal sulcus along each edge of the dorsum; the ligula is short and the apertural rim is flared. The emended concept of Orthotheca includes only those species of orthothecid hyoliths which have a subtriangular transverse outline and longitudinal lirae covering the shell on both dorsum and venter.Eighteen species of Hyolithes and one species of Orthotheca from the Appalachian region and Western Interior were reexamined in light of more modern taxonomic concepts and standards of quality for type material. Reexamination of type specimens of H. similis Walcott from the Lower Cambrian of Newfoundland, H. whitei Resser from the Lower Cambrian of Nevada, H. billingsi Walcott from the Lower Cambrian of Nevada, H. gallatinensis Resser from the Upper Cambrian of Wyoming, and H. partitus Resser from the Middle Cambrian of Alabama indicates that none of these species represents Hyolithes. Hyolithes similis is here included under the new genus Similotheca, in the new family Similothecidae. Hyolithes whitei is designated as the type species of the new genus Nevadotheca, to which H. billingsi may also belong. Hyolithes gallatinensis is referred to Burithes Missarzhevsky with question, and H. partitus may represent Joachimilites Marek. The type or types of H. attenuatus Walcott, H. cecrops Walcott, H. comptus Howell, H. cowanensis Resser, H. curticei Resser, H. idahoensis Resser, H. prolixus Resser, H. resseri Howell, H. shaleri Walcott, H. terranovicus Walcott, and H. wanneri Resser and Howell lack shells and/or other taxonomically important features such as a complete aperture, rendering the diagnoses of these species incomplete. Their names should only be used for the type specimens until better preserved topotypes become available for study. Morphology of the types of H.? corrugatus Walcott and “Orthotheca” sola Resser does not support placement in the Hyolitha; the affinities of these species are uncertain.

scholarly journals Amino acid residues modulating the activities of staphylococcal glutamyl endopeptidases

2010 ◽  
Vol 391 (10) ◽  
Author(s):  
Toshio Ono ◽  
Yuko Ohara-Nemoto ◽  
Yu Shimoyama ◽  
Hisami Okawara ◽  
Takeshi Kobayakawa ◽  
...  
Keyword(s):  
Family Members ◽  
Glutamyl Endopeptidase ◽  
Peptidase Activity ◽  
Amino Acid Residues ◽  
Virulence Determinants ◽  
Cloning And Sequencing ◽  
New Family ◽  
The Family ◽  
N Terminus ◽  
Staphylococcus Epidermis

AbstractThe glutamyl endopeptidase family of enzymes from staphylococci has been shown to be important virulence determinants of pathogenic family members, such asStaphylococcus aureus. Previous studies have identified the N-terminus and residues from positions 185–195 as potentially important regions that determine the activity of three members of the family. Cloning and sequencing of the new family members fromStaphylococcus caprae(GluScpr) andStaphylococcus cohnii(GluScoh) revealed that the N-terminal Val residue is maintained in all family members. Mutants of the GluV8 enzyme fromS. aureuswith altered N-terminal residues, including amino acids with similar properties, were inactive, indicating that the Val residue is specifically required at the N-terminus of this enzyme family in order for them to function correctly. Recombinant GluScpr was found to have peptidase activity intermediate between GluV8 and GluSE fromStaphylococcus epidermisand to be somewhat less specific in its substrate requirements than other family members. The 185–195 region was found to contribute to the activity of GluScpr, although other regions of the enzyme must also play a role in defining the activity. Our results strongly indicate the importance of the N-terminal and the 185–195 region in the activity of the glutamyl endopeptidases of staphylococci.

Palaeonema phyticum gen. n., sp. n. (Nematoda: Palaeonematidae fam. n.), a Devonian nematode associated with early land plants

Nematology ◽  
2008 ◽  
Vol 10 (1) ◽  
pp. 9-14 ◽  
Author(s):  
George Poinar Jr ◽  
Hans Kerp ◽  
Hagen Hass
Keyword(s):  
Early Stage ◽  
Land Plant ◽  
Terrestrial Plants ◽  
Early Devonian ◽  
Plant Parasitism ◽  
New Family ◽  
The Earth ◽  
The Family ◽  
The Face ◽  
Early Land

AbstractNematodes are one of the most abundant groups of invertebrates on the face of the earth. Their extremely poor fossil record hinders our ability to assess just when members of this group invaded land and first became associated with plants. This study reports fossil nematodes from the stomatal chambers of the Early Devonian (396 mya) land plant, Aglaophyton major. These nematodes, which are tentatively assigned to the order Enoplia, are described as Palaeonema phyticum gen. n., sp. n. in the new family Palaeonematidae fam. n. Diagnostic characters of the family are: i) cuticular striations; ii) uniform, cylindrical pharynx with the terminal portion only slightly set off from the remainder; and iii) a two-portioned buccal cavity with the upper portion bearing protuberances. The presence of eggs, juveniles and adults in family clusters within the plant tissues provide the earliest evidence of an association between terrestrial plants and animals and may represent an early stage in the evolution of plant parasitism by nematodes.

Applanodictyosporous Pleosporales: Clathrospora, Comoclathris, GraphyIlium, Macrospora, and Platysporoides

1992 ◽  
Vol 70 (8) ◽  
pp. 1617-1658 ◽  
Author(s):  
R. A. Shoemaker ◽  
C. E. Babcock
Keyword(s):  
Key Words ◽  
New Genus ◽  
New Family ◽  
The Family

Six genera of the order Pleosporales are revised taxonomically. Although five genera have unusual applanate ascospores, they are members of three different families. Clathrospora (10 species, 2 new), Comoclathris (21 species, 7 new), and Macrospora (3 species) are placed in a new family Diademaceae in which the ascoma opening is a characteristic flat circular lid. Diademosa, a new genus with one species with terete ascospores is placed in Diademaceae. Graphyllium (3 species) is placed in the family Hysteriaceae characterized by hysterothecia with a slit-like opening. Platysporoides n.gen. (11 species, 1 new) is maintained in the Pleosporaceae because of the terete pored beak of the ascomata. Key words: Pleosporales, applanate ascospores, Clathrospora, Comoclathris, Macrospora, Diademosa, Graphyllium, Platysporoides.

An Efficient Weighted Residual Time Integration Family

2021 ◽  
pp. 2150106
Author(s):  
Mohammad Rezaiee-Pajand ◽  
S. A. H. Esfehani ◽  
H. Ehsanmanesh
Keyword(s):  
Degrees Of Freedom ◽  
Time Integration ◽  
Nonlinear Damping ◽  
Implicit Methods ◽  
New Family ◽  
Error Analyses ◽  
Damping Behavior ◽  
The Family ◽  
New Strategy ◽  
Time Integration Methods

A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are [Formula: see text] and [Formula: see text] for even and odd values of [Formula: see text], respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.

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