In numerical analysis, the process of fitting a function via given data is called interpolation. Interpolation has many applications in engineering and science. There are several formal kinds of interpolation, including linear interpolation, polynomial interpolation, piecewise constant interpolation, trigonometric interpolation, and so on. In this article, by using Sigmoid functions, a new type of interpolation formula is presented. To illustrate the efficiency of the proposed new interpolation formulas, some ap plications in quadrature formulas (in both open and closed types), numerical integration for double integral, and numerical solution of an ordinary differential equation are included. The advantage of this new approach is shown in the numerical applications section.

Introduction: Inguinal hernias are common diseases in the population, and the prevalence of colorectal cancer has increased significantly in recent decades. However, the concomitant association of these two entities is rarely described in the literature. In most cases, due to the complex diagnosis, patients are treated in emergencies with obstruction or perforation. Nowadays, there is no established consensus on the best surgical approach when this association exists. Case Presentation: We report a case of an 84-year-old patient admitted to the emergency room with a chronic inguinoscrotal hernia, with signs of intestinal obstruction, being diagnosed in the preoperative period by computed tomography, a neoplasm of the Sigmoid colon incarcerated in the hernial sac. The patient underwent radical oncologic surgical treatment and inguinal herniorrhaphy through two access routes, with good postoperative evolution and outpatient follow-up after sixteen months. Conclusions: The association between CRC and inguinal hernia is unusual, but the surgeons should keep this possibility in mind because the treatment must be aimed to accomplish a safe oncologic outcome and as optimal as possible hernia repair.

Background: Sigmoid volvulus is a rare complication in pregnancy. The clinical presentation is similar to that of non-pregnant volvulus, although the symptoms can be masked by the enlarged uterus and physiological changes during pregnancy and it can be challenged and delayed in diagnosis and treatment. Delay in diagnosis can also lead to ischemia, necrosis and perforation of the intestine, which can have adverse maternal and fetal outcomes. Case Presentation: A primigravid woman with gestational age of 31 weeks was admitted to a 3rd level center with abdominal pain and abdominal distention. From the beginning of pregnancy, the patient complained of bloating and epigastric pain, And had used herbal medicine for defecation. The patient's constipation had worsened since six days before admission to the hospital. She had no vomiting and her general condition was good. Abdominal Supine X-rays were reported completely dilated Sigmoid and she was treated with a possible diagnosis of ileus. Due to the progression of symptoms and abdominal distension, rectoSigmoidoscopy was performed for her, and scattered mucosal erythema was seen. Discoloration of the purple mucosa was seen from a distance of about 35 cm from the annulus and the secretions inside the Sigmoid lumen were seen as blood. Ischemic necrosis and Sigmoid volvulus were strongly suggested for the patient and she was immediately transferred to the operating room. The abdomen was opened with a midline incision. A 30 weeks uterus was seen and Sigmoid volvulus was confirmed. Detorsion and colostomy were done. Due to the unprepared intestine and the possibility of leakage from the site of anastomosis, Sigmoidectomy was not performed. After 4 days, the patient was discharged in a good general condition and became a candidate for Sigmoid colon resection after delivery. Conclusion: All abdominal signs and symptoms during pregnancy, especially in late pregnancy have a complex interpretation and management, due to the impossibility of accurate abdominal examination. The most important factors in the proper management of Sigmoid volvulus in pregnancy are fast diagnosis and treatment, hydration and antibiotic therapy.

Lipomas of the gasterointestinal Tract are relatively uncommon in clinical practice. Most cases are asymptomatic with small tumor size and do not need any special treatment but the large ones are known to cause symptoms such as abdominal pain, obstruction, intussusceptions, and bleeding. The majority (90%) of these lesions are submucosal with predominantly right sided with a slight preponderance in females. Recurrence or malignant transformation has not documented in these lesions. We present a case of giant submucosal lipoma in a 33 years old male in Sigmoid colon presenting with abdominal pain and rectal bleeding from Imam Hospitals’ complex, Tehran-Iran. In patients with gastrointestinal symptoms and large mass in Sigmoid and with non-specific findings in colonoscopy, this disease has to be taken into consideration.

Introduction: Heavy metal pollution is one of the most serious environmental problems. These metals which accumulate in food chain bring about a lot of hazards to both humans and animals. Among heavy metals, lead is considered to be the most dangerous heavy metal in the environment. It contaminates the environment through the lead-acid battery industry, paint and gasoline additives, insecticides, chemical fertilizers, car exhaust pipes and soldering. The objective of this study was to investigate the effect of Pb(NO3)2 on germination characteristics and biochemical changes of two wheat cultivars (Chamran and Kohdasht cultivars). Materials and Methods: The objective of this research was to evaluate germination and biochemical changes of two wheat cultivars under Pb(NO3)2 stress, using three-parameter Sigmoid model. The experimental design adopted was factorial with a completely randomized design, as the base design, with 3 replications. The first factor was 2 wheat cultivars (Kohdasht and Chamran), and the second factor was 6 levels of Pb(NO3)2 (0, 0. 25, 0. 5, 0. 75, 1 and 1. 5 mg. L). Results: The results showed that with increases in levels of Pb(NO3)2 stress, germination percentage, germination rate, normal seedling percentage, seedling length, seedling weight and seed vigor index reduced for both wheat cultivars. The results of fitting three-parameter Sigmoidal to characteristics indicated that the highest characteristics and X50 were obtained from the Chamran cultivar. The highest germination percentage (96%), germination rate (23 seeds per day), normal seedling percentage (93. 33%), seedling length (13. 07 cm), seedling weight (0. 07) and seedling vigor index (12. 18) were obtained from the Chamran cultivar under non-stress conditions. Pb(NO3)2 stress increased proline and catalase activity but reduced protein, proline and protein for the Chamran cultivar, as compared with the Kohdasht cultivar. Conclusion: Generally speaking, the results showed that Pb(NO3)2 had a significant effect on germination characteristics and catalase, proline and protein of wheat. Finally, it could be said that in copperaccumulated areas, choosing proper cultivars can slightly mitigate the damages caused by copper. The Chamran cultivar seems to be a better candidate for these conditions.