Intrahepatic and extrahepatic cholangiocarcinomas develops through a multistep carcinogenesis sequence and they are preceded by precursor lesions. Precursors of malignant neoplasm are identified in various organs including uterine cervix, gastrointestinal tract and breast. Identification of these precursor lesions are important in that they need minimal treatment or they are good indicator of d...

We discuss the partial infinite sum ∑∞ k=n u −s k for some positive integer n, where uk satisfies a recurrence relation of order s, un = aun−1 + un−2 + · · ·+ un−s (n ≥ s), with initial values u0 ≥ 0, uk ∈ N (0 ≤ k ≤ s− 1), where a and s(≥ 2) are positive integers. If a = 1, s = 2, and u0 = 0, u1 = 1, then uk = Fk is the k-th Fibonacci number. Our results include some extensions of Ohtsuka and ...

In this study we give recurrence relations of single and product moments of lower record values from modified-inverse Weibull distribution.

We postulate that {Zn} satisfy the recurrence relations (5) E(s^\Fn,z) = K W ] ^ a.s. and for any set of integers l ^ W i < w 2 < • • • <rik with | s t | â l , A MS Subject Classifications. Primary 6067; Secondary 6030.

Abstract Background The prognostic values of inflammation-based markers in well-differentiated pancreatic neuroendocrine neoplasms, diagnosed according to the new 2017 World Health Organization classification, have remained unclear. Therefore, we assessed ability predict recurrence such after curative resection patients with these neoplasms. Methods Circulating/systemic neutrophil–lymphocyte, m...

Introduction: Hilar cholangiocarcinoma is a relatively rare tumor with poor prognosis and few long-term survivors. Although recent advances in imaging diagnosis, surgical techniques, perioperative management can result increased resectability improved outcomes, patients who had operation still have risk of cancer recurrence. Local recurrence, following resection for the bile duct, usually incur...

Consider the sequence of poles A = {α1, α2, . . .}, and suppose the rational functions φn with poles inA form an orthonormal system with respect to an Hermitian positive-definite inner product. Further, assume the φn satisfy a three-term recurrence relation. Let the rational function φ n\1 with poles in {α2, α3, . . .} represent the associated rational function of φn of order 1; i.e. the φ n\1 ...

Anaplastic lymphoma kinase (ALK) rearranged spindle cell mesenchymal tumours are an emerging category of soft tissue neoplasm with variable clinical and pathological features.1–3 We describe a case 6-year-old female who presented pigmented lesion on her abdomen. Biopsy the showed low-grade dermally based prominent storiform architecture, some entrapped collagen focal extension into subcutis. Th...

Herniation of the temporomandibular joint (TMJ) into external auditory canal is rare as TMJ and are separated by an anterior bony wall canal. The defect can be caused trauma, otologic procedure, neoplasm, inflammation a congenital defect. Conservative treatment available if severity symptom mild or asymptomatic. However, surgical procedure considered patient experiences severe distress. There h...