Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Stepwise Increases in Left Ventricular Mass Index and Decreases in Left Ventricular Ejection Fraction Correspond with the Stages of Chronic Kidney Disease in Diabetes Patients

Aims. Patients with diabetic nephropathy are reported to have a high prevalence of left ventricular structural and functional abnormalities. This study was designed to assess the determinants of left ventricular mass index (LVMI) and left ventricular ejection fraction (LVEF) in diabetic patients at various stages of chronic kidney disease (CKD). Methods. This cross-sectional study enrolled 285 diabetic patients with CKD stages 3 to 5 from our outpatient department of internal medicine. Clinical and echocardiographic parameters were compared and analyzed. Results. We found a significant stepwise increase in LVMI (P < 0.001), LVH (P < 0.001), and LVEF <55% (P = 0.013) and a stepwise decrease in LVEF (P = 0.038) corresponding to advance in CKD stages. Conclusions. Our findings suggest that increases in LVMI and decreases in LVEF coincide with advances in CKD stages in patients with diabetes

DYNAMICAL EFFECTS OF SPRINT START ON DIFFERENT STARTING BLOCKS

The purpose of this study was to examine the dynamical variables of sprint start in two different starting blocks setups. The ReacTime Personal Systems was used to record the Reaction Time (RT) and the Power of 20 teenaged sprinters (15 males and 5 females) in the sprint start. In addition, the Newtest Powertimer photocells were used to collect subjects’ 0 to 10 metre (T10) performance after the sprint start. The variables were tested by the repeated measures one-way ANOVA by SPSS 19.0 statistical software at a .05 significant level. The results showed that there were better effects on the short starting block (SB) in power generation performance than the long starting block (LB). The athletes can apply short starting block and make adjustments and modifications based on their training conditions

Theoretical basis, application, reliability, and sample size estimates of a Meridian Energy Analysis Device for Traditional Chinese Medicine Research

OBJECTIVES: The Meridian Energy Analysis Device is currently a popular tool in the scientific research of meridian electrophysiology. In this field, it is generally believed that measuring the electrical conductivity of meridians provides information about the balance of bioenergy or Qi-blood in the body. METHODS AND RESULTS: PubMed database based on some original articles from 1956 to 2014 and the authoŕs clinical experience. In this short communication, we provide clinical examples of Meridian Energy Analysis Device application, especially in the field of traditional Chinese medicine, discuss the reliability of the measurements, and put the values obtained into context by considering items of considerable variability and by estimating sample size. CONCLUSION: The Meridian Energy Analysis Device is making a valuable contribution to the diagnosis of Qi-blood dysfunction. It can be assessed from short-term and long-term meridian bioenergy recordings. It is one of the few methods that allow outpatient traditional Chinese medicine diagnosis, monitoring the progress, therapeutic effect and evaluation of patient prognosis. The holistic approaches underlying the practice of traditional Chinese medicine and new trends in modern medicine toward the use of objective instruments require in-depth knowledge of the mechanisms of meridian energy, and the Meridian Energy Analysis Device can feasibly be used for understanding and interpreting traditional Chinese medicine theory, especially in view of its expansion in Western countries

Examining Symptom Trajectories That Predict Worse Outcomes in Post-CABG Patients

Background: Coronary artery bypass grafting is one of the most common interventional revascularisation procedures used to treat coronary artery disease worldwide. With a wide variability in postoperative cardiac symptoms, identification of symptom trajectories during the 3-month postoperative recovery period may improve clinicians’ abilities to support symptom recovery. Aims: To identify distinct trajectories of cardiac symptoms seen over time in a cohort of patients during the 3-month post-coronary artery bypass grafting period, and determine clinical characteristics associated with different symptom trajectories postoperatively. Methods: A prospective trial used the cardiac symptom survey to determine patient symptoms at baseline prior to surgery, and at 1 week, 6 weeks and 3 months following coronary artery bypass grafting. A latent class growth model and multivariate logistic regression analyses were used. Results: Data were obtained from patients (N=198) undergoing coronary artery bypass grafting in six medical centres of Taiwan, through patient medical records and interviews. Based on their frequency, trajectories were explored for the six most common postoperative symptoms including angina, dyspnoea, fatigue, depression, sleep problems and anxiety. We identified two to three distinct classes of trajectories for each symptom. Age, longer intensive care unit stay, fewer vessels bypassed, off-pump coronary artery bypass grafting, smoking history and lack of regular exercise were associated with worse symptom outcome trends over time. Conclusions: Using this unique trajectories-based research method, we are able to achieve a better understanding of symptom recovery patterns over time among coronary artery bypass grafting patients. Recognising risk factors and potential recovery patterns prior to surgery may allow healthcare providers to deliver targeted discharge planning and individualised care after coronary artery bypass grafting

Urothelial carcinoma in a remnant ureter after a radical nephrectomy for renal cell carcinoma: A case report

AbstractUrothelial carcinoma of a ureteral stump after a radical nephrectomy for renal cell carcinoma is rare. We present the case of a 76-year-old man with painless gross hematuria. The patient had undergone a right nephrectomy for renal cell carcinoma 30 months previously. Cystoscopy showed a blood clot in the right ureteral orifice, and ureteroscopy revealed a papillary mass in the right ureter. The patient underwent a right ureterectomy and bladder cuff resection. The pathology examination showed a high-grade urothelial carcinoma. However, a superficial bladder tumor was discovered postoperatively, and a transurethral resection of the bladder tumor was performed. At 8 months postoperatively, the patient was alive with no evidence of recurrence. A ureteral stump evaluation must be performed when painless hematuria is noted in patients after a nephrectomy