Bailey Type Research Articles

A case of a giant Bailey type I lateral cervical cyst

AbstractBackgroundLateral cervical cysts are among the most frequent branchial anomalies of the neck, although they rarely become large.Case presentationThe present case involved a 32‐year‐old man with swelling of the right side of the neck. Pre‐operative CT findings showed a low CT value on the right side of the neck. Lateral cervical cyst removal was performed under general anesthesia, and the excision was 100 mm × 70 mm × 30 mm, which is the largest ever reported removal of a Bailey type I lateral cervical cyst.ConclusionThe patient had a good clinical course, with no post‐operative recurrence.

ANDREWS’ TYPE WP-BAILEY LEMMA AND ITS APPLICATIONS

ver the years, the study of Bailey transform, Bailey lemma, Bailey pair, their variants and their applications are the major subjects of interest. Of course, it is due to the efficiency of the Bailey transform and lemma in producing many ordinary and q-hypergeometric identities, multiple series summation and transformation formulas, and the Rogers-Ramanujan type identities. Andrews investigated a WP-Bailey lemma and the pairs with the help of Bailey transform and used it to derive well-known summations and multiple series transformations. In this research paper, we investigate an Andrews’ type WP-Bailey lemma and the pairs with the help of First Bailey Type Transform due to Joshi and Vyas. The investigated Andrews’ type WP-Bailey lemma is then applied to obtain terminating multiple q-hypergeometric identities and construct the WP-Bailey type chains and a binary tree. The paper is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including number theory, theory of partitions and combinatorial analysis as well as in the study of combinatorial generating functions.

A Bailey type identity with applications related to integer representations

In this paper we shall deduce a Bailey type formula as a consequence of the residual identity of a q q -series transformation due to Gasper. Our formula leads to a variety of q q -series identities which are related to the arithmetic function counting integer representations of the form \[ n ( A n + B ) 2 + r ( C r + D ) 2 + E n r . \frac {n(An+B)}{2}+\frac {r(Cr+D)}{2} + Enr. \]

Endoscopically assisted transoral resection of a Bailey type IV second branchial cleft cyst

Rationale:The diagnosis of type IV branchial cleft cyst (BCC) according to the Bailey classification is very challenging due to lack of specific clinical manifestations in the early stage of the disease. Here, we present the transoral surgical route of endoscopic resection of second BCC in the parapharyngeal space (PPS) with good outcomes.Patient concerns:A 21-year-old man with a 1-year history of snoring complained about sore throat for 1 month and a fever that lasted for 3 days.Diagnoses:On admission, physical examination revealed a temperature of 39°C, pain when swallowing accompanied with a lump sensation in the throat, and inability to open mouth more than 3 cm. Blood testing revealed 19.29 × 109 white blood cells (WBCs)/L and 14.94 × 109 neutrophils/L. A cervical computed tomography (CT) examination revealed a mass with liquid density of 6.2 × 4.0 × 7.7 cm3 in the left parapharyngeal space (PPS) and pharyngeal cavity stenosis. Postoperative pathology showed the existence of lymphoepithelial cysts (left PPS), which was in accordance with the diagnosis of BCC.Interventions:The patient was administered 1.5 g ceftazidime every 12 hours, anti-inflammatory drugs, and incision drainage was performed subsequently. Then, endoscopy-assisted resection of the left PPS was performed via the transoral route. We used low-temperature plasma and an 8-Fr Foley catheter with a water capsule during the surgery.Outcomes:After resection of the mass, the patient's blood results returned to within the normal range and his symptoms improved. Five days postoperatively, the incision made in the palatine arch of the pharynx opened up by 1 cm, and eventually the wound and laceration healed. Normal oral eating was restored, and no complications were observed.Lessons:Magnetic resonance imaging (MRI), and color Doppler ultrasound can be useful to diagnose BCC in PPS, which rarely occurs in the clinical setting. Extended endoscopy provides a satisfactory surgical field for trans-oral resection allowing complete resection of the BCC without serious postoperative complications.

The Lamps with short and heart-shaped nose and Isparta Museum Examples (Brants Type 18, Loeschcke Type 8, Broneer Type 25, Ponsich Type 4,Bailey Type Q, Bussière D IX-X)

Isparta Müzesi daha çok Pisidia Bölgesi eserlerinin korunduğu önemli bir kent müzesidir. Zengin bir koleksiyona sahip bu müzenin eserleri arasında yer alan kandiller önemli bir grup dikkat çeker. Bugüne kadar ki çalışmalarda müzenin kandilleri sınıflandırılarak kısmen de olsa çalışılmıştır. Bu çalışmada ise burun üzerinde kabartı kalp uygulamasına sahip 10 adet örnek tanıtılmaktadır. Bu eserler 3 alt grup şeklinde değerlendirilir: dairesel formlu ve kulpsuz, dairesel formlu, kulplu ve diskusu bezemeli ve dairesel formlu, kulplu ve diskusu bezemesiz. İrdelenen bu eserler arasında farklı bezeme şemalarına rastlandı. Tipolojide genel form yapısının yanı sıra süsleme detayları da kriter olarak kabul edilmiştir. İrdelenen kandiller arasında bezemesiz örnekler bulunmaktadır. Bunun yanı sıra diskusunda içerisinden asma yaprakları ve üzüm salkımları çıkan krater kabartmalı ya da sıçrayan yunus balığı gibi şemalara sahip örneklerde vardır. Eserler satın alma ya da başka müzeden transfer şeklinde müzeye kazandırılmışlardır. Bu nedenle buluntu alanları belirsizdir. Dolayısıyla üretim yerleri üzerine fazla bir veri ortaya konamamıştır. Buna karşın literatür verileri doğrultusunda bu kandillerin genel olarak 2. yüzyıla tarihlendirildikleri anlaşılmıştır.

The Globular Cluster NGC 6402 (M14). II. Variable Stars*

Abstract We present time-series BVI photometry for the Galactic globular cluster NGC 6402 (M14). The data consist of ∼137 images per filter, obtained using the 0.9 and 1.0 m SMARTS telescopes at the Cerro Tololo Inter-American Observatory. The images were obtained during two observing runs in 2006–2007. The image-subtraction package ISIS, along with DAOPHOT II/ALLFRAME, was used to perform crowded-field photometry and search for variable stars. We identified 130 variables, eight of which are new discoveries. The variable star population is comprised of 56 ab-type RR Lyrae stars, 54 c-type RR Lyrae, 6 type II Cepheids, 1 W UMa star, 1 detached eclipsing binary, and 12 long-period variables. We provide Fourier decomposition parameters for the RR Lyrae, and discuss the physical parameters and photometric metallicity derived therefrom. The M14 distance modulus is also discussed, based on different approaches for the calibration of the absolute magnitudes of RR Lyrae stars. The possible presence of second-overtone RR Lyrae in M14 is critically addressed, with our results arguing against this possibility. By considering all of the RR Lyrae stars as members of the cluster, we derive . This, together with the position of the RR Lyrae stars of both Bailey types in the period–amplitude diagram, suggests an Oosterhoff-intermediate classification for the cluster. Such an intermediate Oosterhoff type is much more commonly found in nearby extragalactic systems, and we critically discuss several other possible indications that may point to an extragalactic origin for this cluster.

Atypical imaging observations of branchial cleft cysts

The aim of the present study was to assess the atypical imaging manifestations of branchial cleft cysts (BCCs) confirmed by pathology. Computerized tomography (CT) or magnetic resonance imaging (MRI) of 17 BCC cases were reviewed. The imaging features, including laterality, location, border, attenuation and internal architecture, were evaluated. All 17 cases were second BCCs, including 5 cases of Bailey type I classification cysts and 12 cases of type II classification cysts. The atypical imaging features included signal and morphological abnormalities. The abnormal signal intensities were caused by intracapsular bleeding (n=2) or solidification of cystic fluid (n=2). Intracystic hemorrhaging revealed homogeneous hyperintensity on T1-weighted image (T1WI) and T2-weighted image (T2WI). Solidification of cystic fluid revealed slightly homogeneous hyperintensity compared with muscle on T1WI and homogeneous hypointensity on T2WI without enhancement. The aberrant morphology mainly presented as thickening of the cystic wall (n=13). Thickened walls of BCCs with ill- (n=5) or well- (n=8) defined borders were observed in 13 patients. In 3 patients, significant enhancement was identified following intravenous gadolinium administration (n=4). When with atypical CT or MRI features are presented, the typical location of BCCs can help in the diagnosis, as it is located at the lateral portion of the neck adjacent to the anterior border of the mandibular angle or sternocleidomastoid muscle. The atypical observations, including variable signals, imply that the cystic content has changed. Thickened walls indicate inflammation or cancerous tendency and patients with ill-defined margins, vascular involvement or lymphadenopathy atelectasis indicate malignant conversion.

Variable stars in the globular cluster NGC 4590 (M68)

We present results of time series photometry to search for variable stars in the field of metal-poor globular cluster NGC 4590 (M68). Periods have been revised for 40 known variables and no significant changes were found. A considerable change in Blazhko effect for V25 has been detected. Among nine newly discovered variable candidates, 5 stars are of RRc Bailey type variables while 4 stars are unclassified. The variable stars V10, V21, V50 and V51 are found to be cluster members based on the radial velocity data taken from literature.

SP0022 Knock-in mice reveal in vivo consequences of MMP activity for OA

We have compared knockin mice with aggrecan and type II collagen resistant to aggrecanases, collagenases, or both families of enzymes, to identify the most important proteolytic driver for cartilage erosion....

Bailey type summation formulas associated with the root system $G_{2}^{\vee}$

We present three types of summation formulas for the root system \(G_{2}^{\vee}\), which are generalized from Bailey’s summation formula for a very-well-poised balanced 6ψ6 basic hypergeometric series.

Bailey type summation formulas associated with the root system [formula omitted

We state three types of hypergeometric summation formulas associated with the exceptional root system F 4 ∨ , which are motivated from Bailey's summation formula for a very-well-poised-balanced ψ 6 6 basic hypergeometric series.

Identities of the Rogers–Ramanujan–Bailey type

A multiparameter generalization of the Bailey pair is defined in such a way as to include as special cases all Bailey pairs considered by W.N. Bailey in his paper [Identities of the Rogers–Ramanujan type, Proc. London Math. Soc. (2) 50 (1949) 421–435]. This leads to the derivation of a number of elegant new Rogers–Ramanujan type identities.

Some dynamical consequences of parasitoid diapause

Parasitoid diapause usually serves to synchronize parasitoids with host populations that are undergoing diapause, to avoid some period of unsuitable conditions. Non‐synchronizing diapause can occur, however, in a number of situations. For example, a fraction of the diapausing parasitoids may stay dormant for a number of seasons. Parasitoids attacking each generation of a multivoltine host may enter a “bank” of diapausing individuals that will emerge at the beginning of the next season. Finally, parasitoid diapause initiation may be driven by density‐dependent processes. I examine the effect of these three scenarios on the stability of Nicholson – Bailey type models. I show that in general, non‐synchronizing parasitoids can potentially have a strong de‐stabilizing influence on parasitoid‐host dynamics.

Q-Difference Equations and Identities of the Rogers–Ramanujan–Bailey Type

In a recent paper, I defined the “standard multiparameter Bailey pair” (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (Proc. London Math. Soc. (2), 50 (1948), 1–10) arose as special cases of the SMPBP. Additionally, I was able to find a number of new Rogers–Ramanujan type identities. From a given Bailey pair, normally only one or two Rogers–Ramanujan type identities follow immediately. In this present work, I present the set of q-difference equations associated with the SMPBP, and use these q-difference equations to deduce the complete families of Rogers–Ramanujan type identities.

Spatial mechanisms for coexistence of species sharing a common natural enemy

We examine the conditions under which spatial structure can mediate coexistence of apparent competitors. We use a spatially explicit, host–parasitoid metapopulation model incorporating local dynamics of Nicholson–Bailey type and global dispersal. Depending on the model parameters, the resulting system displays a plethora of asynchronous dynamical behaviors for which permanent or transient coexistence is observed. We identify a number of spatially mediated tradeoffs which apparent competitors can utilize and demonstrate that the dynamics of spatial coexistence can typically be understood from consideration of two and three patch systems. The phase relationships of species abundances are different for our model than for some other mechanisms of spatial coexistence. We discuss the implications of our findings relative to issues of community organization and biological conservation.

The Intermediate-Period Cepheid Strip Stars

To explore the population of variable stars that fall between RR Lyrae stars and classical Cepheids, we have obtained extensive photometric observations for 56 stars with periods between 0.6 and 1.0 days. For these stars and an additional 10, we have examined the form and stability of the light curves to explore the variety of types of stars in this period regime. We conclude that the majority of the sample are Bailey type ab RR Lyrae stars. However, a surprising number that possibly exhibit the Blazhko effect are found. There are a half-dozen other stars that do not appear to be in either of these two groups. One is the well-known multimode pulsator AC And. We suggest that two of the others may be anomalous Cepheids and two may be type II Cepheids.

RR Lyrae Variables in Local Group Galaxies: M31

AbstractCandidate RR Lyrae variables have been identified for the first time in four globular clusters of the Andromeda galaxy (M31). Using HST-WFPC2 archive observations we have found 2, 4, 11 and 8 RR Lyrae variables of both ab and c Bailey types in G11, G33, G64 and G322 (Sargent et al., 1977), respectively. These numbers are quite consistent with the horizontal branch morphology exhibited by the four clusters.

RR Lyrae Variables in the Globular Clusters of M31: A First Detection of Likely Candidates

The purpose of this paper is to show that RR Lyrae variables exist and can be detected in M31 globular clusters. We report on the first tentative identification of RR Lyrae candidates in four globular clusters of the Andromeda galaxy, i.e. G11, G33, G64 and G322. Based on HST-WFPC2 archive observations in the F555W and F814W filters spanning a total interval of about 5 consecutive hours we find evidence for 2, 4, 11 and 8 RR Lyrae variables of both ab and c Bailey types in G11, G33, G64 and G322, respectively. Several more candidates can be found by relaxing slightly the selection criteria. These numbers are quite consistent with the horizontal branch morphology exhibited by the four clusters, starting from the very blue HB in G11, and progressively moving to redder HBs in G64, G33 and G322.

RR Lyrae Variables in the Globular Cluster M55. The First Evidence for Nonradial Pulsations in RR Lyr Stars

AbstractWe present the results of a photometric study of RR Lyrae variables in the field of the globular cluster M55. We have discovered nine new RR Lyrae stars, increasing the number of known variables in this cluster to 15 objects. Five of the newly discovered variables belong to Bailey type RRc and two to type RRab. Two background RRab stars are probable members of the Sagittarius dwarf galaxy. Fourier decomposition of the light curves was used to derive basic properties of the present sample of RR Lyrae variables. From an analysis of the RRc variables we obtain a mean mass of M = 0.53 ± 0.03 M⊙, luminosity log L = 1.75 ± 0.01 L⊙, Teff = 7193 ± 27 K, and helium abundance Y = 0.27 ± 0.01. We also derive the value of the color excess for M55 to be equal to E(B − V) = 0.11 ± 0.03. We estimate the values of the visual apparent distance moduli to be 13.65 ± 0.11 from RRab stars and 13.91 ± 0.08 from RRc stars. The light curves of three of the RRc variables exhibit changes in amplitude of over 0.1 mag on time scales of less than a week, rather short for the Blazhko effect, but with no evidence for another radial pulsational frequency. However, we do detect other periodicities which are clearly visible in the light curve after removing variations with the first overtone radial frequency. This is strong evidence for the presence of nonradial pulsations, a behavior common for 8 Scuti stars, but not yet observed among RR Lyr variables.

RR Lyrae Variables in the Globular Cluster M55. The First Evidence for Nonradial Pulsations in RR Lyrae Stars

We present the results of a photometric study of RR Lyrae variables in the field of the globular cluster M55. We have discovered nine new RR Lyrae stars, increasing the number of known RR Lyrae variables in this cluster to 15 stars. Five of the newly discovered variables are Bailey type RRc, and two are type RRab. Two background RRab stars are probable members of the Sagittarius dwarf galaxy. Fourier decomposition of the light curves was used to derive basic properties of the present sample of RR Lyrae variables. From an analysis of the RRc variables we obtain a mean mass of M = 0.53 ± 0.03 M⊙, luminosity log L = 1.75 ± 0.01, effective temperature Teff = 7193 ± 27 K, and helium abundance Y = 0.27 ± 0.01. Based on the B-V colors, periods, and metallicities of the RRab stars, we estimate the value of the color excess for M55 to be equal to E(B - V) = 0.11 ± 0.03. Using this value we derive the colors of the blue and red edges of the instability strip in M55. The blue edge lies at (B - V)0 = 0.20 mag, and the red edge lies at (B - V)0 = 0.38 mag. We estimate the values of the visual apparent distance moduli to be 13.65 ± 0.11 from RRab stars and 13.91 ± 0.08 from RRc stars. The light curves of three of the RRc variables exhibit changes in amplitude of over 0.1 mag on the timescale of less than a week, rather short for the Blazhko effect, but with no evidence for another radial pulsational frequency. However, we do detect other periodicities for these three stars that are clearly visible in the light curve after removing variations with the first overtone radial frequency. This is strong evidence for the presence of nonradial pulsations, a behavior common for δ Scuti stars but not yet observed among RR Lyrae variables.