A numerical scheme for the ground state of rotating spin-1 Bose-Einstein condensates.

We study the existence of nontrivial solution branches of three-coupled Gross-Pitaevskii equations (CGPEs), which are used as the mathematical model for rotating spin-1 Bose-Einstein condensates (BEC). The Lyapunov-Schmidt reduction is exploited to test the branching of nontrivial solution curves from the trivial one in some neighborhoods of bifurcation points. A multilevel continuation method is proposed for computing the ground state solution of rotating spin-1 BEC. By properly choosing the constraint conditions associated with the components of the parameter variable, the proposed algorithm can effectively compute the ground states of spin-1 [Formula: see text] and [Formula: see text] under rapid rotation. Extensive numerical results demonstrate the efficiency of the proposed algorithm. In particular, the affect of the magnetization on the CGPEs is investigated.

CD56+ B-cell Neurolymphomatosis in a Cat.

A 16-year-old male Russian blue cat was presented with acute onset of paraparesis of the forelimbs that progressed to tetraparesis. Neurological examination revealed non-ambulatory tetraparesis with decreased postural reactions in all four limbs. Magnetic resonance imaging revealed multifocal nerve root swelling on the right at C6/C7 and C7/T1, while ultrasonography demonstrated swelling of the right brachial plexus. To understand the cause of the nerve swelling, the right musculocutaneous nerve arising from the brachial plexus and the pectoralis muscle were biopsied. Histologically, there was evidence of neurolymphomatosis (neurotropic lymphoma) with Wallerian degeneration and denervation atrophy of myofibres. The neoplastic lymphoid cells expressed CD79a, CD20 and CD56. Based on these findings, a diagnosis of B-cell neurolymphomatosis was made. Expression of CD56, synonymous with neural cell adhesion molecule, is rare in B-cell lymphomas and has not been reported in feline B-cell lymphomas or feline neurolymphomatosis. CD56 expression was suspected to have played an important role in neurotropism of the neoplastic cells in this case.

Turbulence in a matter-wave supersolid.

Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a two-dimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC). When the coupling constant of the soft-core interaction is over a critical value, the superfluid (SF) system can transition into a hexagonal supersolid (SS) state. Based on the Gross-Pitaevskii equation approach, we have discovered a new characteristic k-13/3 scaling law for wave turbulence in the SS state, that coexists with the waveaction k-1/3 and energy k-1 cascades commonly existing in a SF BEC. The new k-13/3 scaling law implies that the SS system exhibits a negative, minus-one power energy dispersion (E ~ k-1) at the wavevector consistent with the radius of the SS droplet. For vortex turbulence, in addition to the presence of the Kolmogorov energy k-5/3 and Saffman enstrophy k-4 cascades, it is found that large amount of independent vortices and antivortices pinned to the interior of the oscillating SS results in a strong k-1 scaling at the wavevector consistent with the SS lattice constant.

Different intestinal tropism of the G2b Taiwan porcine epidemic diarrhea virus-Pintung 52 strain in conventional 7-day-old piglets.

The group 2b (G2b) porcine epidemic diarrhea virus (PEDV) that emerged in 2013 has since caused devastating diseases and economic loss. The full-length genome of the G2b Taiwan PEDV-Pintung 52 (PEDV-PT) strain and its intestinal tropism by evaluating the pathological changes in the original PEDV-PT infected field piglet and orally inoculation of either 10, 103, or 105 50% tissue culture infective dose/mL (TCID50/mL) of the plaque-purified PEDV-PT-Passage 5 (P5) in 7-day-old conventional piglets were analyzed. Phylogenetic analysis of the full-length genome indicated that the G2b Taiwan PEDV-PT strain was closely related to the North American G2b PEDV strains. Some pathological features of the G2b Taiwan PEDV-PT infection, including the absence of lesions and antigen signal in the crypt epithelial cells of the jejunum and ileum and in the villus enterocytes of the duodenum and colon, were different from those of infections by the North American G2b PEDV strains. This difference in the intestinal tropism of the G2b Taiwan PEDV-PT strain highlights the importance of studying the pathogenicities of different PEDV variants. Moreover, similar distributions of PEDV antigens and lesions in the G2b Taiwan PEDV-PT infected field piglet and its plaque-purified isolate, PEDV-PT-P5, inoculated piglets indicating that the plaque-purified PEDV-PT-P5 viral stock could facilitate the preclinical evaluation of vaccines and other interventions aimed at preventing the G2b PEDV infection.

Diffuse-type Gastric Mucinous and Signet Ring Cell Adenocarcinoma in a Captive California King Snake (Lampropeltis getula californiae).

An adult female California king snake (Lampropeltis getula californiae) housed in Taipei Zoo was presented with a 2-week history of anorexia, fatigue and abdominal swelling. Exploratory laparotomy revealed a gastric mass with two circular perforations and multiple mottled white to beige protuberances along the mucosal surface. Histologically, the gastric mass showed an invasive, transmural growth of epithelial cells arranged in nests, lobules, acini and sheets in the mucosa and submucosa that progressively transformed into signet ring cells in the muscularis externa and subserosa. All of the neoplastic cells expressed pan-cytokeratin immunohistochemically. Based on the World Health Organization histological criteria, a diagnosis of diffuse-type gastric mucinous and signet ring cell adenocarcinoma was made.

PBPK Modeling of the Effect of Reduced Kidney Function on the Pharmacokinetics of Drugs Excreted Renally by Organic Anion Transporters.

Altered pharmacokinetics (PK) in subjects with chronic kidney disease (CKD) may lead to dosing adjustment of certain drugs in subjects with CKD. It can be valuable to quantitatively predict PK in CKD for the management of drug dosing in these subjects. We developed physiologically based pharmacokinetic (PBPK) models of seven renally eliminated drugs: adefovir, avibactam, entecavir, famotidine, ganciclovir, oseltamivir carboxylate, and sitagliptin. These drugs are all substrates of renal organic anion transporters (OATs). Drug models verified using PK data from healthy subjects (HS) were coupled with physiological models representing CKD that incorporated prior knowledge of effects of CKD on hepatic and renal elimination. The models reasonably described clinically observed PK changes in subjects with CKD (compared to subjects with normal renal function), with predicted AUC changes within 50% of the observed changes. PBPK models can be used to prospectively predict PK of renally eliminated OAT substrates in subjects with CKD.

Metabolomic and Genome-wide Association Studies Reveal Potential Endogenous Biomarkers for OATP1B1.

Transporter-mediated drug-drug interactions (DDIs) are a major cause of drug toxicities. Using published genome-wide association studies (GWAS) of the human metabolome, we identified 20 metabolites associated with genetic variants in organic anion transporter, OATP1B1 (P < 5 × 10-8 ). Of these, 12 metabolites were significantly higher in plasma samples from volunteers dosed with the OATP1B1 inhibitor, cyclosporine (CSA) vs. placebo (q-value < 0.2). Conjugated bile acids and fatty acid dicarboxylates were among the metabolites discovered using both GWAS and CSA administration. In vitro studies confirmed tetradecanedioate (TDA) and hexadecanedioate (HDA) were novel substrates of OATP1B1 as well as OAT1 and OAT3. This study highlights the use of multiple datasets for the discovery of endogenous metabolites that represent potential in vivo biomarkers for transporter-mediated DDIs. Future studies are needed to determine whether these metabolites can serve as qualified biomarkers for organic anion transporters. Quantitative relationships between metabolite levels and modulation of transporters should be established.

Designing a stronger interface through graded structures in amorphous/nanocrystalline ZrCu/Cu multilayered films.

Many multilayered nano-structures appear to fail due to brittle matter along the interfaces. In order to toughen them, in this study, the microstructure and interface strength of multilayered thin films consisting of amorphous ZrCu and nanocrystalline Cu (with sharp or graded interfaces) are examined and analyzed. The interface possesses a gradient nature in terms of composition, nanocrystalline phase size and volume fraction. The bending results extracted from the nano-scaled cantilever bending samples demonstrate that multilayered films with graded interfaces would have a much higher interface bending strength/strain/modulus, and an overall improvement upgrade of more than 50%. The simple graded interface design of multilayered thin films with improved mechanical properties can offer much more promising performance in structural and functional applications for MEMS or optical coating.

Transition into driven equilibrium of the balanced steady-state free precession as an ultrafast multisection T2-weighted imaging of the brain.

BACKGROUND AND PURPOSE: Current T2-weighted imaging takes >3 minutes to perform, for which the ultrafast transition into driven equilibrium (TIDE) technique may be potentially helpful. This study qualitatively and quantitatively evaluates the imaging of transition into driven equilibrium of the balanced steady-state free precession (TIDE) compared with TSE and turbo gradient spin-echo on T2-weighted MR images. MATERIALS AND METHODS: Thirty healthy volunteers were examined with T2-weighted images by using TIDE, TSE, and turbo gradient spin-echo sequences. Imaging was evaluated qualitatively by 2 independent observers on the basis of a 4-point rating scale regarding contrast characteristics and artifacts behavior. Image SNR and contrast-to-noise ratio were quantitatively assessed. RESULTS: TIDE provided T2-weighted contrast similar to that in TSE and turbo gradient spin-echo with only one-eighth of the scan time. TIDE showed gray-white matter differentiation and iron-load sensitivity inferior that of TSE and turbo gradient spin-echo, but with improved motion artifacts reduction on qualitative scores. Nonmotion ghosting artifacts were uniquely found in TIDE images. The overall SNRs of TSE were 1.9-2.0 times those of turbo gradient spin-echo and 1.7-2.2 times of those of TIDE for brain tissue (P < .0001). TIDE had a higher contrast-to-noise ratio than TSE (P = .169) and turbo gradient spin-echo (P < .0001) regarding non-iron-containing gray matter versus white matter. TIDE had a lower contrast-to-noise ratio than turbo gradient spin-echo and TSE (P < .0001) between iron-containing gray matter and white matter. CONCLUSIONS: TIDE provides T2-weighted images with reduced scan times and reduced motion artifacts compared with TSE and turbo gradient spin-echo with the trade-off of reduced SNR and poorer gray-white matter differentiation.

Occurrence and distribution of Naegleria species from thermal spring environments in Taiwan.

UNLABELLED: Naegleria spp. is a free-living amoeba that can be found in the natural environment. A number of Naegleria spp. can cause fatal infections in the central nervous system in humans and animals, and the most important source of infection is through direct water contact. In this study, water samples from various thermal springs were taken from four thermal spring areas. Naegleria spp. was detected via culture confirmation and molecular taxonomic identification. Among the 60 samples obtained, Naegleria spp. was identified in 26 (43·3%) samples. The identified species included Naegleria australiensis, Naegleria gruberi, Naegleria lovaniensis and Naegleria mexicana. The presence of living Naegleria spp. was significantly associated with elevated pH value in the water sample. SIGNIFICANCE AND IMPACT OF STUDY: In this study, we examined the presence of living Naegleria spp. in thermal spring waters in south-eastern Taiwan. Naegleria spp. was isolated and culture-confirmed from thermal spring water. Naegleria fowleri was not found in all water samples, and Naegleria australiensis was the most common Naegleria genotype.

Piston-on-three-ball versus piston-on-ring in evaluating the biaxial strength of dental ceramics.

OBJECTIVES: Piston-on-three-ball tests have been selected by the International Organization for Standardization to establish ISO 6872 for the evaluation of the biaxial strength of dentistry-ceramic materials. However, the formula adopted in ISO 6872 for the fracture load-biaxial strength relationship was an approximate equation originally derived for piston-on-ring tests of monolayered discs. This formula was modified and extended to the case of multilayered discs subjected to piston-on-ring loadings recently. The purpose of the present study is to evaluate the adequacy of applying the formula for piston-on-ring to piston-on-three-ball tests for both monolayered and multilayered discs. METHODS: Finite element analyses were performed to simulate both piston-on-three-ball and piston-on-ring tests. Different degrees of friction between the specimen supporting surface and the loading fixture were considered in the simulations. The simulated biaxial stress distributions through the disc thickness for both tests were then compared to the formula to examine how the predictions agree. RESULTS: Examples of monolayered, bilayered and trilayered discs subjected to piston-on-three-ball and piston-on-ring loadings were simulated for comparison with the formulae. The results depended on friction when the disc was supported by a ring, however the results became insensitive to friction when the disc was supported by three balls. For the frictionless contact, both loading tests yield almost the identical biaxial stress distribution through the disc thickness and agree well with the formula. On the other hand, the maximum tensile stress on the surface of the disc decreased when the friction increased. As a result the biaxial tensile strength was overestimated for piston-on-ring tests if friction was neglected. SIGNIFICANCE: The results of our finite element analyses demonstrate how the friction between the specimen supporting surface and the loading fixture affects the biaxial strength evaluation in piston-on-ring and piston-on-three-ball tests. It is critical to have frictionless contact between the disc and the supporting ring when evaluating the biaxial strength by piston-on-ring tests. Otherwise, the application of the approximate formula, which was derived for piston-on-ring, to piston-on-three-ball is even better than piston-on-ring. This is true for not only monolayered discs but also multilayered discs.

CT Angiographic Diagnosis of a Ruptured Intraventricular Arteriovenous Malformation in a Teenager Playing a Video Game.

Intraventricular arteriovenous malformation (AVM) is a rare congenital vascular disorder that is often associated with primary intraventricular hemorrhage (IVH) and a rapid clinical course. Acute imaging diagnosis requires depiction of both the location of hemorrhage and vascular nidus for emergent management. In this report, a 17-year-old teenager developed primary IVH with presentation of consciousness change during a video game. Multidetector-row computed tomographic angiography (CTA) demonstrated an AVM in the right lateral ventricle and its angioarchitectural relationship to the surrounding intracranial structures. Although selective angiography is essential both in planning treatment for cerebral AVMs and in establishing the final diagnosis, CTA can be an important first-line imaging modality to quickly confirm the diagnosis and hence initiate prompt management.

The antiapoptotic protein, FLIP, is regulated by heterogeneous nuclear ribonucleoprotein K and correlates with poor overall survival of nasopharyngeal carcinoma patients.

Heterogeneous nuclear ribonucleoprotein K (hnRNP K) mediates antiapoptotic activity in part by inducing downstream antiapoptotic genes. To systematically identify hnRNP K targets in nasopharyngeal carcinoma (NPC), affymetrix chips were used to identify genes that were both overexpressed in primary NPC and downregulated by hnRNP K knockdown in NPC-TW02 cells. The resulting gene set included the antiapoptotic gene, FLIP, which was selected for further study. In cells treated with hnRNP K siRNA, TRAIL-induced apoptosis was enhanced and the FLIP protein level was reduced. Promoter, DNA pull-down and chromatin-immunoprecipitation assays revealed that hnRNP K directly interacts with the poly(C) element on the FLIP promoter, resulting in transcriptional activation. Through iTRAQ-mass spectrometric identification of proteins differentially associated with the poly(C) element or its mutant, nucleolin was determined to be a cofactor of hnRNP K for FLIP activation. Furthermore, FLIP was highly expressed in tumor cells, and this high-level expression was significantly correlated with high-level hnRNP K expression (P=0.002) and poor overall survival (P=0.015) as examined in 67 NPC tissues. A multivariate analysis confirmed that FLIP was an independent prognostic factor for NPC. Taken together, these findings indicate that FLIP expression is transcriptionally regulated by hnRNP K and nucleolin, and may be a potential prognostic and therapeutic marker for NPC.

Prediction of conversion from clinically isolated syndrome to clinically definite multiple sclerosis according to baseline MRI findings: comparison of revised McDonald criteria and Swanton modified criteria.

BACKGROUND: The International Panel on the Diagnosis of Multiple Sclerosis first incorporated abnormalities demonstrated by brain and spinal cord MRI into the diagnostic criteria (McDonald criteria) for multiple sclerosis (MS), which were later revised in 2005. In 2006, Swanton and colleagues modified the MRI criteria to simplify and speed the diagnosis. OBJECTIVE: The purpose of this study was to compare the ability of two sets of criteria (the revised McDonald MRI criteria and Swanton's modified criteria) to predict conversion from clinically isolated syndrome (CIS) to clinically definite multiple sclerosis (CDMS) from baseline MRI findings. METHODS: Sixty-four patients presenting with CIS suggestive of multiple sclerosis were recruited from 2001 to 2006 and followed up for at least 2 years. Their baseline brain and spinal cord MRI studies were retrospectively evaluated. The patients who developed CDMS during follow-up were treated as positive cases. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and accuracy of the two MRI dissemination-in-space criteria were calculated. RESULTS: Thirty patients (46.9%) converted to CDMS. The sensitivity specificity, PPV, NPV and accuracy (%) of the revised McDonald criteria were 53, 100, 100, 71 and 78, respectively, while those for Swanton's modified criteria were 60, 100, 100, 74 and 81. CONCLUSIONS: In conclusion, Swanton's modified criteria are more sensitive and accurate (but not significantly so). However, Swanton's criteria are simpler to use and have equally high specificity and PPV.

Thymidine phosphorylase mRNA stability and protein levels are increased through ERK-mediated cytoplasmic accumulation of hnRNP K in nasopharyngeal carcinoma cells.

The cytoplasmic level of heterogeneous nuclear ribonucleoprotein K (hnRNP K) is significantly correlated with the elevated expression of thymidine phosphorylase (TP), and high levels of both proteins are predictive of a poor prognosis in nasopharyngeal carcinoma (NPC). We herein show that TP is highly induced by serum deprivation in NPC cells, and that this is due to an increase in the half-life of the TP mRNA, as shown by nuclear run-on and actinomycin D assays. We further show that the CU-rich element of the TP mRNA directly interacts with hnRNP K, as demonstrated by immunoprecipitation RT-PCR assays, and the nucleus-to-cytoplasm translocation of hnRNP K. Blockade of hnRNP K expression reduces TP expression, suggesting that hnRNP K acts in the upregulation of TP. Mechanistically, both MEK inhibitor and the hnRNP K ERK-phosphoacceptor-site mutant decrease cytoplasmic accumulation of hnRNP K, suggesting that ERK-dependent phosphorylation is critical for TP induction. Furthermore, we found that hnRNP K-mediated TP induction allows NPC cells to resist hypoxia-induced apoptosis. Our results collectively establish the regulation and role of ERK-mediated cytoplasmic accumulation of hnRNP K as an upstream modulator of TP, suggesting that hnRNP K may be an attractive candidate as a future therapeutic target for cancer.

Simple solutions of multilayered discs subjected to biaxial moment loading.

OBJECTIVES: The purpose of this study was to derive a simple closed-form solution for the stress distribution through the thickness of multilayered discs subjected to biaxial moment loading, such that it can be used readily to evaluate the biaxial strength of multilayered dental ceramics using biaxial flexure tests. METHODS: A simple analytical model was developed to derive the stress distribution through the thickness of multilayered discs subjected to biaxial moment loading. The accuracy of the solution was verified by comparing with previous rigorous analytical solutions and finite element results. The results obtained from Roark's formulas for bilayered discs were also included for comparison. RESULTS: Examples of porcelain/zirconia bilayered discs subjected to ring-on-ring and piston-on-ring loadings were used for comparison among different analyses. Despite the simplicity in deriving the present solution, it is sufficiently accurate in comparing with previous rigorous solutions and finite element results. Also, if the biaxial stresses on the top and the bottom surfaces of the disc can be measured during testing, the biaxial stress/strain through the entire thickness of the multilayered disc can be determined using equations derived in the present model. SIGNIFICANCE: International Organization for Standardization has selected piston-on-three-ball tests to establish ISO 6872 for dentistry-ceramic materials. However, monolayered specimens are considered in tests for this standard. While dental materials are usually fabricated into layered structures, modification of the current standard is essential. Our simple closed-form solution serves as a basis for extending the current standard to multilayered systems.

Endovascular procedures for cerebrovenous disorders.

Cerebral venous anomalies may have a variety of clinical consequences. MR or CT venogram can assist the imaging diagnosis; yet, cerebral angiogram may be required to confirm or establish the correct diagnosis. Venous anomalies predisposing venous hypertension may be categorized into three major entities such as congenital variations, outflow obstruction, and increased blood flow. The degree of clinical presentations of venous hypertension depends upon the chronicity or acuteness. Venous hypertension may lead to venous congestion with edema, hemorrhage and encephalopathy. Endovascular therapeutic procedures may be employed to relieve venous congestion either from reducing blood flow or relieving obstruction. Those endovascular treatment options include embolization, thrombolysis and angioplastic stentings.

Analyses of layer-thickness effects in bilayered dental ceramics subjected to thermal stresses and ring-on-ring tests.

OBJECTIVES: The purpose of this study was to analyze the stress distribution through the thickness of bilayered dental ceramics subjected to both thermal stresses and ring-on-ring tests and to systematically examine how the individual layer thickness influences this stress distribution and the failure origin. METHODS: Ring-on-ring tests were performed on In-Ceram Alumina/Vitadur Alpha porcelain bilayered disks with porcelain in the tensile side, and In-Ceram Alumina to porcelain layer thickness ratios of 1:2, 1:1, and 2:1 were used to characterize whether failure originated at the surface or the interface. Based on (1) the thermomechanical properties and thickness of each layer, (2) the difference between the test temperature and the glass transition temperature, and (3) the ring-on-ring loading configuration, the stress distribution through the thickness of the bilayer was calculated using closed-form solutions. Finite element analyses were also performed to verify the analytical results. RESULTS: The calculated stress distributions showed that the location of maximum tension during testing shifted from the porcelain surface to the In-Ceram Alumina/porcelain interface when the relative layer thickness ratio changed from 1:2 to 1:1 and to 2:1. This trend is in agreement with the experimental observations of the failure origins. SIGNIFICANCE: For bilayered dental ceramics subjected to ring-on-ring tests, the location of maximum tension can shift from the surface to the interface depending upon the layer thickness ratio. The closed-form solutions for bilayers subjected to both thermal stresses and ring-on-ring tests allow the biaxial strength of the bilayer to be evaluated.

Diffusion-tensor MR imaging for evaluation of the efficacy of hyperbaric oxygen therapy in patients with delayed neuropsychiatric syndrome caused by carbon monoxide inhalation.

The purpose of this study is to assess the efficacy of hyperbaric oxygen therapy (HBOT) in patients with delayed neuropsychiatric syndrome (DNS) caused by carbon monoxide (CO) inhalation using diffusion tensor magnetic resonance (MR) imaging and neuropsychological test. Conventional and diffusion tensor brain MR imaging exams were performed in six patients with DNS immediately before and 3 months after the HBOT to obtain fractional anisotropy (FA) values. Six age- and sex-matched normal control subjects also received MR exams for comparison. Mini-Mental State Examination (MMSE) was also performed in patients immediately before and 3 months after the HBOT. A significantly higher mean FA value was found in control subjects as compared with the patients both before and 3 months after the HBOT (P < 0.001). The mean FA value 3 months after the HBOT was also significantly higher than that before the HBOT in the patient group (P < 0.001). All of the patients regained full scores in the MMSE 3 months after the HBOT. Diffusion tensor MR imaging can be a quantitative method for the assessment of the white matter change and monitor the treatment response in patients of CO-induced DNS with a good clinical correlation. HBO may be an effective therapy for DNS.

Appraisal of formulas for stresses in bilayered dental ceramics subjected to biaxial moment loading.

OBJECTIVES: The purpose of this study was to compare three existing sets of formulas predicting stresses in a thin circular plate subjected to biaxial moment loading, such that limitations for each set of formulas could be understood. These formulas include American Society for Testing and Materials (ASTM) formulas for monolayered plates, Roark's formulas for bilayered plates, and Hsueh et al.'s formulas for multilayered plates. METHODS: The three sets of formulas were summarized and appraised. Biaxial moment loading is generally achieved using biaxial flexure tests, and the plate is placed on a support ring and loaded in the central region. While both ASTM and Hsueh et al.'s formulas predict stresses through the thickness of the plate, Roark's formulas predict stresses only on the top and the bottom surfaces of the plate. Also, a simply supported plate at its edge is considered in Roark's formulas. We modified Roark's formulas to include the overhang region of the plate to more closely simulate the actual loading configuration. Then, the accuracy of formulas was examined by comparing with finite element results of monolayered and bilayered plates subjected to ring-on-ring loading. RESULTS: Monolayer is a special case of bilayer, and both monolayer and bilayer are special cases of multilayer. For monolayered plates, ASTM and Hsueh et al.'s formulas are identical, and both are in excellent agreement with finite element results. For bilayered plates, Hsueh et al.'s formulas are in excellent agreement with finite element results. For both monolayered and bilayered plates, Roark's formulas deviate from finite element results while the modified Roark's formulas are accurate. CONCLUSIONS: Roark's formulas for evaluating the biaxial strength of bilayered dental ceramics will result in errors in predicted stresses which depend on the size of the overhang region of the plate in the actual loading configuration. Also, Roark's formulas are limited to predicting stresses on the top and the bottom surfaces of the plate. On the other hand, Hsueh et al.'s formulas are for multilayered plates and predict stresses through the plate thickness.