In the French pedagogic tradition of Gaspard Monge, geometry was learned by drawing and handling models: drawing was knowing. The formalism of the early twentieth century placed illustration on the si...

**Authors:** Kleitos Papadopoulos We study single-item lot sizing with piecewise-concave production and holding--backlog costs over $T$ periods. Production has $m$ common positive finite breakpoints, and stock costs and domains have $K$ common finite boundary levels. For fixed $m,K$, we give an exact deterministic algorithm using $\OmK(T^{m+2}α(T+2))$ arithmetic operations and a Las Vegas algorithm using $\OmK(T^{m+2})$ expected operations, where $α$ is the inverse Ackermann function. The algorithms retain nonlinear concave cost pieces and cover backlogging, common-grid stock limits, and explicit terminal-stock policies. A structural decomposition at stock boundary levels yields breakpoint-only prefix and suffix tables. Batching transitions by a designated production period produces implicit matrices that are Monge double staircases on each production piece. Established matrix searches, merged state orders, and backward evaluation provide the bounds. A simpler rectangle/SMAWK variant requires $\OmK(T^{m+2}\log(T+2))$ operations. On 300 no-backlogging benchmark cases, its objectives agree exactly with the predecessor dynamic program and an inventory-state oracle. Geometric-mean paired time ratios are \GeoUncap\ for uncapacitated cases and \GeoCap\ for capacitated cases, with ratios above one favoring matrix searching. A 640-case base-model validation suite and a separate 624-case generalized-model suite pass. The timing study does not benchmark the generalized models or the stronger staircase routines. All bounds assume exact arithmetic, constant-time cost queries, and explicit closed-domain concavity conditions.

Alt: gif: Homem termina seu TED Talk agradecendo a presença das pessoas com uma dancinha engraçada.

# ¡MÉXICO PEGA DURO EN EL RING! LOGAN HERNÁNDEZ Y RENÉ CALIXTO SE CORONAN, MIENTRAS FERNANDA MONGE ARRASA CON NAYLEA GIL El boxeo mexicano tuvo una jornada de resultados importantes, con triunfos que dejaron nuevos campeones y una victoria de alto calibre en territorio japonés. Sebastián “Logan” Hernández derrotó por decisión dividida a Kyonosuke Kameda en Osaka, mientras que en Hermosillo, René “Indio” Calixto conquistó el campeonato NABO Norteamérica de peso Mosca de la OMB frente a José Luis “Diamante” Russell; además, Fernanda “Chatita” Monge se proclamó campeona Internacional Supermosca del CMB tras vencer por nocaut a Naylea “Niña” Gil.

# ¡MÉXICO PEGA DURO EN EL RING! LOGAN HERNÁNDEZ Y RENÉ CALIXTO SE CORONAN, MIENTRAS FERNANDA MONGE ARRASA CON NAYLEA GIL El boxeo mexicano tuvo una jornada de resultados importantes, con triunfos que dejaron nuevos campeones y una victoria de alto calibre en territorio japonés. Sebastián “Logan” Hernández derrotó por decisión dividida a Kyonosuke Kameda en Osaka, mientras que en Hermosillo, René “Indio” Calixto conquistó el campeonato NABO Norteamérica de peso Mosca de la OMB frente a José Luis “Diamante” Russell; además, Fernanda “Chatita” Monge se proclamó campeona Internacional Supermosca del CMB tras vencer por nocaut a Naylea “Niña” Gil.

11K likes, 763 comments - neto.monge on October 3, 2026: "A democracia precisa alcançar também quem está na linha de frente. Presos provisórios e adolescentes internados possuem mecanismos específico...