Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus

Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral

Hydrogel Implant Causing Lumbar Radiculopathy: A Case Report

Objective: One of the new treatment methods for lumbar degenerative disc disease is percutaneous application of a hydrogel implant into the intervertebral disc. The aim of this method is to increase the disc height, to widen the neural foramen, and to decrease discogenic pain and leg pain caused by root compression. However, there may be serious complications related to intervertebral hydrogel implants that have been increasingly used during the last few years because of their minimally-invasive nature. A case with lumbar root compression due to hydrogel implant is being reported.Case Report: A 61-year-old male was admitted with severe left leg pain due to compression of the left L5 root by a hydrogel implant that had been percutaneously introduced into the L4-5 disc level 6 months ago. On magnetic resonance imaging, a lesion compressing the left L5 root at the L4-5 disc level and mimicking a disc herniation was seen. It was hypointense on T1-weighted and hyperintense on T2-weighted sections. The implant was removed by an open surgery.Conclusion: An intervertebral hydrogel implant swells up by absorbing water from adjacent tissues. Actually, this is the main mechanism of action by which it provides an increase of disc height. However, if it swells up excessively, it may spill over through the spinal canal and thus cause root or dural sac compression and neurological compromise

Cervical Spinal Cord Injury in Patients with Cervical Canal Stenosis without Radiologic Evidence of Trauma: Evaluation of 15 Consecutive Cases

Objective: Cervical spinal canal stenosis is a well-known risk factor for spinal cord injury. In some patients, spinal cord injury is the first symptom of spinal stenosis. Therefore, some authors recommend preventive decompression of the spinal canal in asymptomatic patients with spinal stenosis. In this study, we aimed to determine the outcome of patients with spinal cord injury associated with cervical spinal canal stenosis and the rate of previously asymptomatic patients.Material and Methods: Data of 15 consecutive patients were evaluated. Improvement of neurological deficits during followup was accepted as good outcome and mortality and unchanging neurological deficits were accepted as worse outcome.Results: All patients were male, aged between 44 and 85 years. High-energy traumas caused injury in 7 of the cases and low-energy traumas in the others. Nine cases had central cord injury and 6 had other types of traumas. Only 2 patients had been diagnosed with minor symptoms associated with cervical canal stenosis before trauma, while the other patients had been asymptomatic. One patient did not consent to undergo an operation and two others could not be operated because of their general status; the latter 2 patients died. The other 12 patients were decompressed 0 to 40 days after trauma. Two other patients with severe transverse-type cord injury also died postoperatively. The other patients were followed for 1 to 48 months (22.7±17.7 months). In 2 patients, neurological deficits had not improved on last follow-up. Deficits had completely or partly improved in the other patients, including the one who had not accepted the operation. Central cord injury had a significantly better prognosis than other types (p=0.0019). Age, cervical canal diameter, and motor and sensory scores of the American Spinal Injury Association scale, type of trauma, and level of spinal cord injury were not significantly different in the patients with good and worse prognosis.Conclusion:The rate of asymptomatic patients before trauma was very high in patients with spinal cord injury associated with cervical spinal canal stenosis. Therefore, the treatment decision must be carefully assessed in asymptomatic cervical spinal stenosis patients. Catastrophic consequences of spinal trauma may be seen in patients with cervical spinal canal stenosis even in asymptomatic patients. Central cord syndrome had a good prognosis in these patients. Other types of injuries such as transverse and motor types had a worse outcome

Clinical Outcomes and Factors Affecting the Outcome of Decompressive Craniectomy: Analysis of 50 Cases

Objective: Decompressive craniectomy (DC) is used as the last-stage method in the treatment of increased intracranial pressure (ICP). However, clinical outcomes reported in the literature are contradictory.Methods: Medical records were retrospectively reviewed for 50 increased ICP cases that had been diagnosed and undergone DC at our hospital between February 2011 and February 2017. The patients’ characteristics such as age, sex, presence of comorbidities, pre- and postoperative Glasgow Coma Scale (GCS) scores, blood pressure, hemoglobin values, radiological findings, DC time, width of craniectomy, length of stay in the intensive care unit (ICU), and Glasgow Outcome Scale (GOS) were recorded. According to their outcome, the patients were divided into two groups with good (GOS = 4-5) and poor (GOS = 1-3) prognosis, respectively, according to their last examination. It was evaluated whether these parameters showed significant differences between the groups and between the deceased patients and survivors.Results: A total of 50 patients (35 male and 15 female) had been treated with DC. The mean age was 40.5±22.2 years. Head trauma was the etiology of increased ICP in 68% of the cases (n=34). The median of preoperative GCS was 6 (range: 3-15), and the mean midline shift on admission was 10.3±5.1 mm. Seventy-two percent of the cases (n=36) were treated with DC on the day of admission from the emergency department. The median of postoperative GCS was 7 (range: 3-15). The patients were followed up for a mean of 24.4 days in the ICU, and 30 patients were lost after a mean of 24.6 days. The survivors were followed up for a mean of 7.4±12.5 months. Factors affecting survival periods were age of the patient, short edge length of the DC (not long edge) and early postoperative GCS score after the DC. The comparison between survivors and deceased patients showed that the mean age of survivors was significantly lower than that of deceased patients (p=0.047). Postoperative GCS scores after DC were significantly lower in the patients who had died (p=0.0001).Conclusion: Age, short edge length of the craniectomy and postoperative neurological status are factors affecting surgical outcomes. These factors can play a role in selecting patient candidates who have to receive DC

Sudden Onset of Tetraparesis During Taking of Magnetic Resonance Imaging in a Patient with Undiagnosed Cervical Spinal Stenosis: A Case Report

Objective: To report a case with sudden-onset tetraparesis during taking magnetic resonance imaging (MRI).Case report: A 73-year-old man was referred with complaints of paresis of his arms and legs. His tetraparesis had developed suddenly while an MRI was performed 10 days before. He had a severe tetraparesis with 0/5 motor strength in his legs and 2/5 motor strength in his arms. On the MRI, a serious spinal stenosis at C3-4 and C4-5 levels and a faint myleopathic signal of the spinal cord at the level of the C4-5 disc space were seen. After posterior decompression, the patient’s tetraparesis improved gradually and he could walk independently and perform his daily activities with mild spasticity after 13 months.Conclusion: It is known that sudden neurological deficits may be seen in cervical trauma in patients with cervical spinal stenosis due to spondylosis. However, this case who did not have a trauma history showed us that a long period of positioning the neck beyond the patient’s control, even during the execution of MRI, may cause sudden deterioration

The Optimal Orchestration of Packaging for Sustainability

This study proposes two new mathematical models. These models aim to determine optimal ratio of using package for minimum waste in the environment. The models determine package usage ratios which minimize the packaging wastes when packaging amount is at maximum level in the environment. Models are distinguished from each other ignoring or not ignoring decay of each package in nature themselves. Proposed theoretical mathematical models have real world applications based on genuine data. These models easily can used by any enterprise which is concerned with environment and struggles to minimize the packaging waste

Tourism Destination: Design of Experiences

Purpose - The aim of this chapter is to offer a conceptual model for tourist experiences in the destination and suggest implications for different stakeholders in creating experiences for tourists

A Blood Bank Location Model: A Multiobjective Approach

This effort derived a mathematical programming model, which is a hybrid from set covering model of discrete location approaches and center of gravity method of continuous location models, for location of blood banks among hospitals or clinics, rather than blood bank layout in health care institutions. It is initially unknown the number of blood banks will be located within capacity, their geographical locations and their covering area. The solution of the model enlightens the initial darkness in a multiobjective view. The objectives, which are handled via binary nonlinear goal programming, are minimizitation of total fixed cost of location blood banks, total traveled distance between the blood banks and hospitals and an inequality index as a fairness mechanism for the distances. A hypothetical numerical example is solved using MS Excel as a powerful spreadsheet tool. The recipe, which is an application of medical operations research, may be a useful tool for health care policy makers

Ginger for Healthy Ageing: A Systematic Review on Current Evidence of Its Antioxidant, Anti-Inflammatory, and Anticancer Properties.

The world's population is ageing at an accelerated pace. Ageing is a natural, physiological but highly complex and multifactorial process that all species in the Tree of Life experience over time. Physical and mental disabilities, and age-related diseases, would increase along with the increasing life expectancy. Ginger (Zingiber officinale) is a plant that belongs to the Zingiberaceae family, native to Southeast Asia. For hundreds of years, ginger has been consumed in various ways by the natives of Asian countries, both as culinary and medicinal herb for the treatment of many diseases. Mounting evidence suggests that ginger can promote healthy ageing, reduce morbidity, and prolong healthy lifespan. Ginger, a well-known natural product, has been demonstrated to possess antioxidant, anti-inflammatory, anticancer, and antimicrobial properties, as well as an outstanding antiviral activity due to a high concentration of antiviral compounds. In this review, the current evidence on the potential role of ginger and its active compounds in the prevention of ageing is discussed