Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

Dynamical Behavior of some families of cubic functions in complex plane

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function such that have two critical points and three fixed points such that is attracting when is origin point As shown in figure (2).And are attracting when is the region specified by open disc shown in figure (1.(c)).Second function such that have two critical points and three fixed points such that is attracting when and that its path is to the origin point as shown in figure (4).And are attractive when represents the open disc shown in the figure (3.(c)).Third function such that have one critical point and three fixed points is attracting that is path is the origin point and are repelling as shown in figure (5). And all 2-cycles of are repelling and unstable . http://dx.doi.org/10.25130/tjps.24.2019.139

A new species of Glyphis Ach. and three new records of Graphis Adans. (Graphidaceae) from Bali Island, Indonesia

Glyphis batuana Hardini, Kasiamdari & Purnomo sp. nov. is a new species of lichenized fungus found on the bark of the Frangipani tree (Plumeria sp.). The new species from Batuan village (Gianyar districts), Bali Island, Indonesia is described and illustrated. It is characterized by its lirelliform, unbranched ascomata, entire labia, black, open disc with brown pruina, completely carbonized excipulum, 8-spored asci with 8-10 locular ascospores, and lack of secondary substances. A key to species of Glyphis Ach. in Indonesia is provided. Three new records of Graphis Adans., namely G. conferta Zenker, G. immersella Mull. Arg. and G. nilgiriensis Adaw. & Makhija are also reported.

The lichen genera Allographa and Graphis (Ascomycota: Ostropales, Graphidaceae) in Thailand—eleven new species, forty-seven new records and a key to all one hundred and fifteen species so far recorded for the country

We provide an updated account on the genera Graphis s.str. and Allographa (formerly included in Graphis) from Thailand. Four species of Allographa are described as new to science, viz. A. atrocelatoides, which differs from A. atrocelata in having marginata-morph lirellae and a smooth, off-white to beige thallus; A. kansriana, which differs from A. aquilonia in having negrosina-morph lirellae and brownish ascospores; A. schummii, which is characterized in having large, muriform ascospores and an open disc with a cinnabar-red pruina, reacting K+ lemon yellow; and A. sitianoides, which differs from A. sitiana in having immersed to erumpent lirellae and longer ascospores with more numerous septa. Twenty-seven further species are being recombined in the genus Allographa, viz A. acharii, A. aquilonia, A. atrocelata, A. elongata, A. hossei, A. leptospora, A. lumbricina, A. macella, A. marginata, A. norvestitoides, A. nuda, A. pavoniana, A. phaeospora, A. rhizicola, A. rimulosa, A. rufopallida, A. rustica, A. sauroidea, A. seminuda, A. semirigida, A. striatula, A. subdisserpens, A. subdussii, A. trichospora, A. verminosa, A. vestitoides, and A. xanthospora. Seven new Graphis species are described, viz. G. albocarpa, which differs from G. glaucescens in having a laterally to completely carbonized exciple, larger ascospores, and a norstictic acid chemistry; G. emersella, which differs from G. emersa in having hossei-morph lirellae and smaller ascospores with fewer septa; G. khaojoneana, which differs from G. bungartzii in having immersed, unbranched lirellae and smaller ascospores with fewer septa; G. omiana, which differs from G. luluensis in having larger ascospores with more numerous septa and a more complex chemistry relating to the stictic acid aggregate; G. schummiana, which differs from G. anfractuosa in having a laterally to completely carbonized exciple and in the reddish brown pruinose, K+ purple disc; G. sublitoralis, which differs from G. litoralis in having scripta-morph lirellae and in lacking protocetraric acid; and G. subschroederi, which differs from G. schroederi in having smaller ascospores and a laterally carbonized exciple. Four new lirellae morphs are defined, viz. filiformis-morph, balaghatensis-morph, leptogramma-morph and schummiana-morph. After several collecting trips to nineteen provinces of the country, further forty-seven new records of the two genera are added to the most recent checklist of Thai lichens. A key is given to all Allographa and Graphis species so far known for Thailand, as well as close-up photographs of the newly described or newly reported species. The following ten names are removed from the most recent Thai checklist: Graphis concolor ≡ Diorygma junghuhnii, G. fissurinoidea = Diorygma confluens, G. glaucocinerea = Graphis aphanes, G. glaucorufa = Allographa rufopallida, G. irosina = Acanthothecis dialeuca, G. longispora = G. koratensis, Graphis nuda (probably a misidentification), G. ochrocheila ≡ Dyplolabia ochrocheila, G. persimilis = Phaeographis hypoglauca, and G. subrigida = Platygramme platyloma. Graphis siamensis does not belong in this genus but is likely a species of Phlyctis. Graphis diplocheila has a clear hymenium and is a younger synonym of G. streblocarpa and G. dracaenae produces norstictic acid and must therefore kept apart from G. geraensis.

Certain classes of analytic functions defined by fractional q-calculus operator

In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.

Coefficient Estimates for Certain Subclasses of Biunivalent Functions Defined by Convolution

We introduce two new subclasses of the function class Σ of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients a2 and a3 for the two subclasses are obtained. Moreover, we verify Brannan and Clunie’s conjecture a2≤2 for our subclasses.

Ozone disc nucleolysis as an alternative to open disc surgery for slip disc

Back pain associated with herniated disks has become an important and increasingly general health problem, both in Bangladesh and across the world. After all methods of conservative treatment have been exhausted, nucleolysis may be a minimally invasive alternative to surgery. In nucleolysis, chondrolytic substances, or other substances which reduce the pressure within the disk by other means, are injected into the nucleus pulposus under CT scan or fluroscopic guidance. Among various substances, which have been employed for nucleolysis, an ozone-oxygen mixture appears to be very promising. The water-binding capacity of ozone results in a reduction of pain. Moreover, it has an anti-inflammatory effect and results in an increase in perfusion to the affected area. Ozone is converted into pure oxygen in the body and has a low allergic potential. Recent minimally invasive therapeutic methods such as percutaneous nucleotomy or laser treatment have not been shown to be superior when compared with ozone nucleolysis. DOI: http://dx.doi.org/10.3329/bmj.v43i1.21380 Bangladesh Med J. 2014 January; 43 (1): 51-55